Introduction. The observed 'island universes' or galaxies in the Universe exhibit not only clustering, but also super-clustering, vast line-like structures, walls and voids, and gigantic streaming rivers of galaxies. These unexpected large-scale features raise three questions in the search for empirically-testable, scientific cosmologies. (1) Would these titanic structures require more cosmic time to interact and form than allowed by the current ΛCDM concordance edition of the HBBC (~13.8 Gya)? (2) Are there peculiar features of these survey maps which indicate that there is a non-Hubble relation component contributing to the redshifts of some of the galaxies in clusters and super-clusters? (3) Are there any data suggesting that the temperature fluctuations of the CMB are connected with the large-scale structure of the Universe?

The answers to all three of these questions are likely to be, Yes!

In this section, we will briefly examine how large-scale inhomogeneities, anisotropies, and structures increasingly depart from the requirements of the ΛCDM concordance HBBC paradigm. 

In history, the tensions between human cosmological beliefs and the contrasting emerging empirical data have been centuries long! Gradually humankind has increasingly discovered the macroscopic structures of the World around us, always against some restrictive cosmological mythology (link). The ongoing cosmological demotion of humankind as more and more insignificant has been continuing apace, despite some notable attempts to rehabilitate human centrality.

Conceptions of medieval views juxtaposed with a Hubble view of the Whirlpool Galaxy: This image is paradigmatic of the mix of belief conceptions and actual observed data which have long comprised human cosmologies (https://www.space.com/13336-universe-history-structure-evolution-infographic.html).	The new Ptolemaic system of the HBB Cosmology: A mix of some of the data observations with a predominant model and set of assumptions, including multiple adjustable parameters in the concordance LCDM edition of the Big Bang. The emerging data call this dominant model at least into some question on a variety of points.
One of the great leaps forward was Eratosthenes determined the spheric geometry and estimated the diameter of Earth.
Based on simplistic and completely ad hoc assumptions, the "inflation" scalar field of the early cosmos was supposed to smooth out any large inhomogeneities which would otherwise emerge to an incredibly fine-tuned tolerance. Of course, as Neil Turok and other colleagues have shown,"inflation" does no such thing, and in fact, is completely useless to solve the 'horizon' and 'flatness' problems it was invented ad hoc to resolve. How long do such cosmic structures take to form? Discounting cosmic expansion, the age can be calculated roughly by such structures using A =R/v, where A is the age in years, R is the radius of the structure in light-years, and v is the maximum velocity within the structure as a fraction of c, the velocity of light in a vacuum. For a more complex formula, see Ceccarelli et al. (2006), MNRAS 373, 1440. https://doi.org/10.1111/j.1365-2966.2006.11129.x. Given the constraints of the HBBC, astronomer Joe Silk (October, 1988) stated, "If one measured a gradient or large void that extended over a thousand megaparsecs [~3.26 Gly], then I think he or she would have to seriously question the big bang theory" from "Oral history interview with Joseph Silk," https://www.aip.org/history-programs/niels-bohr-library/oral-histories/38283. According to the Hunt & Sarkar (2010) extrapolation, Silk's estimated upper limit may be >3 times too large.	According to the Planck 2018 interpretation of the CMB data, with dark matter, dark energy, and inflation, i.e., the ΛCDM concordance, the Universe is ~13.813± 0.038 Ga old, while Hubble relation estimates of Cepheid variables suggest an age of about ~12.8± 0.2 Ga old (discussed in link).   Hunt & Sarkar (2010), MNRAS 401, 547 (doi:10.1111/j.1365-2966.2009.15670.x) showed that the ΛCDM big bang model has an upper limit of between ~250 and ~300 Mpc or (~820 and nearly ~1 Gly) at most for possible structure size formation, observing with the two graphs cross each other below. (Conversion: 1 parsec = 3.2615637771675 light-years; Unitchefs).

Further summaries of the status of understanding scale and structure of the Universe may be found at the Atlas of the Universe website, to which we may return again: http://www.atlasoftheuniverse.com/.

In January of 2022, the new Dark Energy Spectroscopic Instrument (DESI) completed it's first 7 months of it's 5 year mission, and has already broken all 3D galaxy survey records, completing about 10% of the area it is going to map. DESI has about 5000 robotically-positioned optic fibers on 8 inch focal plane of the 4 meter Mayal Telescope (Kitt Peak). The most recent survey covers:

(https://www.astro.princeton.edu/universe/; DESI's 3D map of the Universe so far, link).

The question of the Cosmological Principle & its predictions. Going back to an early formal statement of the notion with Isaac Newton's Philosophiæ Naturalis Principia Mathematica (1687) the principle relates to the heliocentric cosmos of the Solar System and beyond to the 'fixed stars' within an empty space stretching uniformly away in all directions in indefinitely large volumes, yielding a law of 'universal gravitation' (link). In modern cosmology, the cosmological principle is rooted in the Friedmann-Lemaître-Robertson-Walker (FLRW) metric (pseudo-Riemannian manifold, as in 4d space-time) foundational to the HBBC, including in it's ΛCDM concordance model, where the entire cosmos is enmeshed in such a uniformly expanding 4d space-time manifold. In this case, in which one finds good 'null hypothesis' test predictions (one of the best features of the HBBC, setting aside all of the ΛCDM epicycles), there must be a cosmological principle thus:

• Cosmological Principle: At sufficiently large (i.e., representative) scales, the Universe must contain a spatial distribution of mass-energy which is (a) homogeneous (uniform at every point without any irregularities larger than scale) and (b) isotropic (uniform in all directional orientations without irregularities larger than scale) because the same laws of physics operate at every point. In the CSSC or classic steady-state cosmology, specifically the Bondi-Gold version (1948), the Cosmological Principle becomes the Perfect Cosmological Principle, which also makes the same predictions except that "the Universe must contain a spatial-temporal distribution of mass-energy which is.... (a) ... and (b)..." because the same physical laws operate at every point and at every time; and so on. This likewise forms a good 'null hypothesis test' prediction. In sum, at representatively large scales, the Universe is homogeneous and isotropic for all observers throughout space (in the HBBC), and back across time (in the CSSC).
  

Between the null hypotheses of the FLRW HBBC Cosmological Principle (setting aside for the moment all of the epicycles) and the Bondi-Gold CSSC Perfect Cosmological Principle, we have four distinct, broad categories of predicted options, which can now be tested by observations as they relate to large scale structures observed in the Universe, and used to suggest more sophisticated cosmologies for the 21st century and beyond. The broad categories of prediction:

• A homogeneous and isotropic Universe.
  
• An inhomogeneous and isotropic Universe.
  
• An homogeneous and anistropic Universe.
  
• An inhomogeneous and anistropic Universe.
  

Here are a few illustrations to summarize (link). By defining homogeneity and isotropy by simple illustrations, we can examine suspected departures from either and from both in the large-scale Universe, which could serve as empirical tests and limits on cosmology models.

Homogeneity (left) and Isotropy (right).

The homogeneous and isotropic scenario where there is no privileged observer position other than galaxies' spin axes orientation (left below), whereas a situation where there is anisotropy in a monodirectional permeation of the cosmos with density and rarefaction waves in the distribution of galaxies (right below), such as could be predicted by "Bianchi universe" models which have homogeneity but departures from isotropy (Schucker, 2016. The Hubble diagram in a Bianchi I universe. https://arxiv.org/pdf/1601.04965.pdf; http://www.scholarpedia.org/article/Bianchi_universes).

Two simple cases where the observer indeed has a privileged position, but where the view outward from it exhibits isotropic density variations in observer centered structures. 

With that, we turn to summarizing observations which suggest departures at observable, representative scales from the Cosmological Principle in a HBBC model, from both homogeneity and from isotropy.

I. The question of Homogeneity: Discovery of large-scale structures & departures from concordance homogeneity. At the beginning of the 20th century, the confirmed structure of the Universe was our Milky Way galaxy and little was known beyond. Over the decades of the second half of the 20th century, modern astronomy has found that galaxy clusters are arranged in a series of described superclusters separated by large intergalactic voids. A pattern that first began to be detected in large photographic surveys of the skies. We step back in time to review these findings and then move forward in time to the latest discoveries. (We examine several of large-scale structures and great voids in cosmic structure found in recent decades: link).

Animation of galactic cluster structure
(https://giphy.com/gifs/just-to-clarify-this-wasnt-a-request-t88QJMxn1taSY).

Angular distribution of clusters of galaxies from the Milky Way galactic plane:

 

(astro.uchicago.edu/~coble/talks/pop_cosmo/grand.xy.pdf).

Of these, the Coma supercluster is one of the largest with over 10,000 galaxies and a length of more than 1.37 billion light years (Image: Springel et al., 2006; cit. in Joseph, 2010b. in the now defunct Journal of Cosmology, Vol 6, 1548-1615), which is > ~1 Gly size limit.

An even more distant view of filamentous wall structuring of the Universe in the 2dF Galactic Redshift Survey, looking out to about 3.5 billion light-years (Richard Powell, Atlas of the Universe; http://www.atlasoftheuniverse.com/universe.html).

How were these superclusters and large wall-&-void structures discovered? And leading to ultimately, how were they formed?

(1) Gigantic-scale structures. The Center for Astrophysics (CfA) surveys of extragalactic redshifts were begun in 1977 by Marc Davis, John Huchra, Dave Latham, and John Tonry (Harvard U / Smithsonian Astrophysical Observatory, SAO) "The first CfA Survey, completed in 1982, (Huchra, Davis, Latham and Tonry, 1983, ApJS 52, 89) had as its goal the measurement of radial velocities for all galaxies brighter than 14.5 and at high galactic latitude in the merged catalogs of Zwicky and Nilson (the UGC)" (http://www.cfa.harvard.edu/~huchra/zcat/).  The first slice of sky spectroscopically surveyed included ca. 1100 galaxies in a region of sky 6 degrees wide and ~130 degrees long, with Earth at the apex of the wedge, done by Valerie de Lapparent, Margaret Geller, and John Huchra (see table above for the reference).

As Huchra described it, "This initial map was quite surprising, showing that the distribution of galaxies in space was anything but random [or homogeneous], with galaxies actually appearing to be distributed on surfaces, almost bubble like, surrounding large empty regions, or 'voids.'"

(http://www.cfa.harvard.edu/~huchra/zcat/).

The CfA2 'Great Wall' and the Sloan Great Wall (discussed below) together (link).

Already in 1986, Brent Tully (University of Hawaii) reported superclusters of 300 X 100 mllion light-years in size, which at current galactic velocities would have taken 80 Ga to assemble (Tully, 1986; Lal, 2010). By superimposing six contiguous slices of 6 degrees of sky each, the CfA Redshift Survey team uncovered "the Great Wall" of galaxies 600 X 250 X 30 million light years in size (Geller and Huchra 1989, Science 246, 897), which would require at least 100 Ga to form according to some estimates (Lal, 2010). The Geller-Huchra "Great Wall" of galaxies discovered in a survey out to z ~ 0.03 is ~200 Mpc, i.e., ~650 Mly. From the very earliest of these angular / redshift survey mappings (even in the first CfA slice above, a strange phenomena began to be observed, galaxies clustered by redshift exhibited a tendency to form oriented stringers or 'fingers' trailing back toward the observer in a peculiar effect whimsically called the "fingers of god" pointing back at Earth, which has been explained as the result of peculiar velocities within the cluster, not explaining of course, why they should be oriented toward Earth observers. We will return to this phenomenon later.

The 'fingers of god' phenomenon had also been observed in 1986, including in Abell clusters of galaxies, which are clusters of >30 galaxies which are often very compact frequently with aging stellar populations, and fairly low redshift values, named after a northern hemisphere survey done in American astronomer George Abell in 1958, and since extended to the southern hemisphere. The 'fingers of god' effect turns out to be less dramatic in the aging Abell clusters than in clusters containing younger galaxies with active galactic nuclei (AGNs), which has definite implications for galactic cosmogony:

Figure adapted from Narlikar (1993). Introduction to Cosmology (2nd edition). Cambridge, UK: Cambridge University Press; p. 20.

The CfA2 survey also revealed the inhomogeneous clustering and the 'fingers of god' phenomenon.    

The CfA2 survey of vaster reaches of the Universe, also exhibited the inhomogenous clustering and the 'fingers of god' phenomenon.

The redshift distribution of the CfA2 (Center for Astrophysics 2) survey can also be seen in this polar projection of the redshifts for all the galaxies in the CfA2 survey out to 12,000 km/s. This is a section of a cylinder in equatorial coordinates looking down from the north pole to the equator with a height of 12,000 km/s and a radius of 12,000 km/s. Tha major structures seen are again the Local Superluster just above the middle of the plot, the Great Wall cutting from 9 hours and 5,500 km/s to 15 hours and 9,000 km/s and the Pisces-Perseus supercluster centered around 1 hour and 4,000 km/s. The geometry of this projection is similar to that of a hockey puck (http://cfa-www.harvard.edu/~huchra/zcat/).

Here is the 2001 CfA2 survey with redshift results color-coded by estimated Doppler velocities of recession:

Although these gigantic structures seemed to create difficulties at the time for the HBB Cosmology, especially given the very smooth CMB radiation as understood then, there were much larger violations of homogeneity, which have strained and then violated the predictions of the HBBC even further. In the CfA2 survey mapping, the "fingers of god" phenomenon continued to be present, especially at the lower redshift values.

In 2003 and 2004, Tegmark et al. released, The 3D power spectrum of galaxies from the SDSS. https://arxiv.org/abs/astro-ph/0310725, and then published in 2004, The three-dimensional power spectrum of galaxies from the Sloan Digital Sky Survey. ApJ 606 (2), 702. https://doi.org/10.1086/382125, a summary paper which sought to measure the large-scale real-space power spectrum P(k) of galaxy distribution within the SDSS in a set of 205,433 galaxies with an average redshift of z ≈ 0.1 over 2417 degrees square of the sky. The power spectrum was not found to have a single power law (i.e., requires some parameter-fitting). The postulate is that there is a P(k) ∝ k^n-1, a Fourier transform where k is the wave number of the perturbation (link), which they wished to measure so as to compare with then recent WMAP measurements of the CMB (Bennett et al. 2003. First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Preliminary maps and basic results. arXiv (v3): https://arxiv.org/abs/astro-ph/0302207. ApJ Suppl Series 148 (1), 1-27. https://doi.org/10.1086/377253) for useful measurements of cosmological model parameters. They wished to find corrections to distortions in redshift space yielding well-behaved functions in the range of 0.02 h/Mpc < k < 0.3 h/Mpc up to "some unknown multiplicative bias factor" which they argue they calculated to be scale-independent or scale-invariant "better than a few percent for k < 0.1 h/Mpc." The authors claim that their measurements are "well fit by a flat scale-invariant adiabatic cosmological model with hΩ_m = 0.213 ± 0.023 and σ₈ = 0.89 ± 0.02 for L∗ galaxies, when fixing the baryon fraction Ω_b/Ω_m = 0.17 and the Hubble parameter h = 0.72" which they went on to interpret in what they called the companion paper. In this paper, the authors sought to account for (1) "complicated survey geometry," and correct for (2) redshift-space distortions, (3) artificial red-tilt based on luminosity bias, and (4) potential systematic errors. These corrections include dealing with the 'fingers of god' effect, which will be discussed more below.

In axonometric representation (3d structure represented on a 2d plane orthogonal to the line of sight), the "Great Sloan Wall" megacluster of galaxies looks like this:

The Great Sloan Wall in projected 3d (Gott et al. 2005).

Another vast structure (discovered in 2020) is the "South Pole Wall" (approaching ~400 Mpc or ~1.31 Gly), a structure comparable in size to the "Great Sloan Wall" but half the distance away (Pomarede et al. 2020. Cosmicflows-3: The South Poll Wall. ApJ 897, 133. https://iopscience.iop.org/article/10.3847/1538-4357/ab9952; https://doi.org/10.3847/1538-4357/ab9952).

Although the Cosmicflows-3 velocity and structure density reconstructions are derived from model-based ΛCDM concordance adjustable parameters of Ω_m = 0.3, Ω_Λ = 0.7, and a H₀ = 75 km s^-1 Mpc^-1, even then, these density reconstructions imply some very huge structures indeed at variance with concordance expectations, implying even vaster and more connected structures than the authors seem willing to explicitly state, and possibly not showing the entire structure, some excluded by Milky Way galactic zones of obscuration, but implied by a potential continuity of the data delimited.

Figures 1 and 5 reconstruct the structure of the South Pole Wall with its scale, implying that it is part chosen from a larger structure. Figure 5 illustrates that it is indeed considered as a subset chosen somewhat arbitrarily from a greater whole (cf. Fig. 1). The reconstruction model restricts the peculiar velocity contours within certain ranges (see accompanying figure legends) which suggests that the superstructure was constrained by exclusion of some peculiar velocity field components. This would be even more significant an edit if one considers that these structures may be gravitationally open in the Ambartsumian sense.

Figure 3 reconstruction to scale compares the South Pole Wall (SPW) with the previously discovered CfA2 Great Wall and the Sloan Great Wall. Such huge structures occur in both the northern skies and the southern skies. The SPW is significant because it is a much more local superstructure.

The Figure 4 peculiar velocity restricted reconstruction within the galactic frame of reference implies that there is more to the overall superstructure (resembling the quasi-spherical shells of density) of which the South Pole Wall is but a part.

The Figure 6 reconstruction combines two models of peculiar velocities implied from distance. The black wire grid reconstructs the location of the South Pole Wall within a larger structure. If this is all one super structure, then it might well be roughly ~500-550 Mpc (~1.6 - ~1.8 Gly) in extent, massively outside the concordance homogeneity limit.  

The reconstruction in Figure 2 suggests that the same structure reaches from the south galactic hemisphere into the northern galactic hemisphere too, across the zone of Milky Way galactic obscuration. 

The Figure 8 reconstruction combines the large scale structure with the estimated velocity flow lines within that overall structure:

Still from video linked on https://www.livescience.com/giant-arc-in-space.html.  The cluster of South Pole Wall galaxies and its connections to the various local clusters and structural features (cf. https://www.livescience.com/south-pole-wall-discovered-in-space.html; https://en.wikipedia.org/wiki/South_Pole_Wall).

Of this unusually vast structure, the authors admit, "We will not be certain of its full extent, nor whether it is unusual, until we map the universe on a significantly grander scale." This indicates that we don't know how large the great South Pole Wall of galaxies actually is, or how common such are. Despite this, Princeton astrophysicist Neta Bahcall (wife of the late John Bahcall), and unconnected with the Pomarede et al. research published, is strangely cited as confidently asserting in the popular Live Science article that "Knowing how the universe looks on such large scales helps confirm our current cosmological models" while it actually rather raises more questions about those current models. She is quoted as going on to pile on to that assertion this almost unintelligible (if in context) quote, "When you look at the network of filaments and voids, it becomes a semantic question of what's connected" (Link). These data hardly raise semantic issues as much as they raise substantive questions about the prevailing cosmology.

Another immensely huge structure (~3.3 Gly across) and ~9.2 Gly distant is called the "Giant Arc" of galaxies stretching across about 1/15th of the observable part of the Universe, with an 0.0003% probability of being artifactual. Using Mg-absorption patterns of light from distant quasars, Alexia Lopez et al. discerned this arc structure (07 June 2021 presentation at the 238th meeting of the American Astronomical Society, AAS, which has since been turned into a paper): Lopez, A. M., Clowes, R. G., & Williger, G. M. 2022. A giant arc in the sky. https://arxiv.org/abs/2201.06875. MNRAS 516 (2), 1557-1572. https://doi.org/10.1093/mnras/stac2204.

The Giant Arc with grey regions indicating areas with magnesium (Mg) absorbance showing the presence of galaxies / galaxy clusters,
while blue patterns (blue dots on the L, and blue contours on the R) show the presence of QSOs.

The placement of the Giant Arc in our night sky:
 

(https://www.livescience.com/giant-arc-in-space.html;
https://www.vice.com/en/article/g5gjzm/a-structure-in-deep-space-is-so-giant-its-challenging-standard-physics).

Lopez' doctoral advisor, Roger Clowes, opined in the context of the increasing number of huge structures discovered, "They're so large, you wonder if they're compatible with the cosmological principle" (link), which in the HBBC context would dictate a size limit to such structures, but Pomarede, the French cosmographer who discovered the South Pole Wall, pointed out, "Instead, we keep finding these bigger and bigger structures." In order to have a cosmological principle (homogeneity and isotropy at sufficiently large scales) within the HBBC ΛCDM model with a 1/H₀ age of ~13.8 Gya, there is a theoretical limit by some lights of about 1.2 Gly maximum size for such structures. Of course, there is no need to immediately consider abandoning the cosmological principle, if one is allowed to consider older and vaster models than the HBBC ΛCDM. Furthermore, if the cosmological principle is to be abandoned, then the HBBC ΛCDM is also on the way out. This website highlights evidence suggestive of such.

In January of 2024, the same scientific team with doctoral student, Alexia Lopez (link) and advisor Prof. Roger Clowes, presented at the American Astronomical Society (AAS) another giant structure at the same Hubble redshift distance in the same overall direction separated by ~12, which they have called the 'Big Ring' (10 January 2024). The 'Big Ring' is also ~9.2 Gly distant, with a diameter of ~1.3 Gly and a circumference of ~4 Gly. Both the 'Giant Arc' and the 'Big Ring' (actually more like a corkscrew coil) are larger than the maximum ~1.2 Gly size of structures predicted in standard HBBC / ΛCDM cosmology. In February 2024, the paper was released: Lopez, A. M., Clowes, R. G., & Williger, G. M. 2024. A big ring in the sky. https://arxiv.org/abs/2402.07591; https://www.researchgate.net/publication/378157464_A_Big_Ring_on_the_Sky.

The Big Ring which is actually more of a corkscrew, with the gray spots representing the Mg II absorbers at z = 0.802 0.060, considered to be in the tangent-plane at a set distance of the Ring, while the small blue dots represent the putative background probes or quasars (L, Fig. 1). Fig. 2 (on the R) shows the identified Mg II absorbers within the Ring (blue dots). 

(https://phys.org/news/2024-01-discovery-ultra-large-distant-space.html; cf. https://www.bbc.com/news/science-environment-67950749; https://www.uclan.ac.uk/news/big-ring-in-the-sky; story in The Guardian; https://www.space.com/big-ring-galactic-superstructure-celestial-anomaly).
 

In an article containing an interview, "A big cosmological mystery," released by her own University of Central Lancashire (UCLan) media (https://www.uclan.ac.uk/news/big-ring-in-the-sky; 11 January 2024), Alexia Lopez had this to say,

"Cosmologists calculate the current theoretical size limit of structures to be 1.2 billion light-years, yet both of these structures are much larger – the Giant Arc is almost three times bigger and the Big Ring’s circumference is comparable to the Giant Arc’s length. "From current cosmological theories we didn't think structures on this scale were possible. We could expect maybe one exceedingly large structure in all our observable universe. Yet, the Big Ring and the Giant Arc are two huge structures and are even cosmological neighbours, which is extraordinarily fascinating.... "The Big Ring and Giant Arc are the same distance from us, near the constellation of Boötes the Herdsman.... Identifying two extraordinary ultra-large structures in such close configuration raises the possibility that together they form an even more extraordinary cosmological system. "

The UCLan article also suggests that these size violations of the 'Big Ring' are outside of the ΛCDM predictions, and canvas the idea that something like the Conformal Cyclic Cosmology (CCC) model of the group around Nobel Laureate Sir Roger Penrose have proposed (which we discuss in our Chapter V. The Cosmic Microwave Background (CMB) radiation: From Where and Whence? "As far as the eye can see?" along with other alternative cosmological models). If Alexia Lopez is correct that both the 'Giant Arc' and the 'Big Ring' or 'big cork screw' are associated in a super-structure, then that could be on the order of ~4 Gly in diameter or more. This again shows violations of structure-size limitations within a HBBC / ΛCDM model, and to question the Cosmological Principle of heterogeneity and isotropy of our observable Universe, whether these assumptions work on the scale of our observable horizon. If not, then standard cosmology must be questioned.

Gamma-Ray Burst (GRB) aggregations. Another even more vast set of structures have been tentatively revealed through distant aggregations of gamma ray burst (GRB) events illuminating huge, remote structures. GRBs are considered to be the most energetic stellar explosions in the Universe. They are durationally short (from milliseconds to a few hours) and they are considered to be distributed in accordance with the cosmological principle, being thought to be across the skies with large-scale homogeneity and isotropy. They are hypothesized to result from the core collapse of supermassive stars into neutron stars and stellar blackholes, and also the mergers of neutron stars / stellar black holes with each other.

The data on GRBs was collected by the orbiting Compton Gamma Ray Observatory (CGRO, link, wikipedia) collecting data from 1991-2000 in the 20 keV to 30 GeV region of the spectrum. One of the projects, called the Burst and Transient Source Experiment (BATSE; link) searched across the sky for gamma-ray bursts (20 to >500 keV) finding more than 2700 events:

Angular locations of GRBs in the skies with their color-coded energies (Compton Gamma Ray Observatory legacy, 2016;
https://asd.gsfc.nasa.gov/blueshift/index.php/2016/04/13/lookingbackcgro/), exhibiting rather high levels of apparent homogeneity.

An artist's conception of a bright GRB in an active star-burst region within a galaxy
(https://en.wikipedia.org/wiki/Gamma-ray_burst).

From the BATSE project, "the complete spectral catalog of bright BATSE gamma-ray bursts" has been published by Kaneko et al. [2006; ApJ Suppl. Series 166 (1), 298. https://iopscience.iop.org/article/10.1086/505911/pdf]. A follow-up space observatory specializing in gamma ray burst astronomy is the Neils Gehrel Swift Observatory (https://swift.gsfc.nasa.gov; cf. link) launched in 2004, which does not contain an acronym, 'swift' being a reference to the rapid observing times, like the swift type of bird. The Swift program has produced a catalog of GRBs, with a burst analyzer complementary site. There is also a transient notice site and Swift trigger and burst real-time information site.  An interesting early finding suggesting something unusual in distribution that GRBs at certain regions of the sky would indicate possible vast structures violating homogeneity assumptions as well as isotropy assumptions inherent in the HBBC / ΛCDM models of the cosmological principle. The cosmological principle (CP, the large-scale homogeneity and isotropy of the Universe) is sometimes held to depend on limit at the very outermost of a transition scale limit of the largest possible structures which don't violate the CP: 370 Mpc (~1.207 Gly). Of course this limiting of the scale "below which the CP is valid" is arbitrary in part because it is HBBC model-dependent.

In 2014, Horvath and colleagues published results from a 2012 measurement of the redshifts of 283 GRBs (Possible structure in the GRB sky distribution at redshift two. A&A 561, L12. https://doi.org/10.1051/0004-6361/201323020). They found that there was an enrichment of GRBs in a particular direction of the sky in this redshift range,1.6 < z < 2.1, which clustered in a statistically-significant aggregation, passing three statistical tests: Nearest neighbor, 2d Kolmogorov-Smirnoff, and a Bootstrap Point-Radius Method. This structure ~10 Gly away (10x farther than the Sloan Great Wall and 6x larger) has dimensions of about 2000-3000 Mpc (~ 6.5 - 9.8 Gly), i.e., far beyond the HBBC ΛCDM size limit.

Figure 3 note: On a projection of the Galactic celestial sphere, the 283 GRBs in total are essentially homogeneous and isotropic in their distribution (blue squares = yellow squares in inversion). The Galactic extinction region along the Galactic plane is represented by the lightly mottled or stippled equatorial zone. Earth's ecliptic polar regions (pink mottled = green mottled in inversion) are over-sampled due to the GRB orbiting observatory Swift's sky view. The 31 GRBs in the 1.6 < z < 2.1 redshift range exhibit a striking anisotropy (prominent red crosses = greenish in inversion).

A preliminary 2013 paper presented at the 7th Huntsville Gamma Ray Burst Symposium (GRB 2013) by Horvath et al. (The largest structure of the Universe, defined by Gamma-Ray Bursts, paper 33 in eConf Proceedings C1304143; https://arxiv.org/abs/1311.1104) showed their early identification of the GRB structure, with a binomial probability of such an angular anisotropy to be artifactual at only p = 0.0000055. 

283 GRBs with measured redshifts (blue = yellow inverted) and the 31 GRBs in the 1.6 < z < 2.1 zone (red = teal).

Another enormous GRB structure is the so-called "giant GRB ring-like" aggregate of 9 GRBs, discovered in the 0.78 < z < 0.86 range, at a distance of 2770 Mpc (~9.03 Gly) covering an angular size of 43 by 30 degrees, (Balazs et al. 2015. A giant ring-like structure at 0.78 < z < 0.86 displayed by GRBs. MNRAS 452 (3), 2236. https://doi.org/10.1093/mnras/stv1421; arXiv: https://arxiv.org/abs/1507.00675). This implies that the ring-like structure is about 1720 Mpc (~5.61 Gly) in size, thus "large enough to contradict the CP [cosmological principle]" as the authors point out in their abstract, with a p = 2 x 10^-6 probability of being "a random fluctuation in the GRB count rate." The authors go on to state that "the physical mechanism responsible for causing it is unknown." One not terribly daring thought emerging is that this is yet another "anomaly" for the HBBC ΛCDM theory.

The very largest structures so far showing violations of homogeneity on a colossal scale involved pencil-beam 1 degree wide surveys in the Hubble Deep Field, North (HDF-N) and the Hubble Ultra Deep Field (HUDF), and were published by a Russian group, Shirakov et al. (2016). Large-Scale Fluctuations in the Number Density of Galaxies in Independent Surveys of Deep Fields. Astronomy Reports 60 (6), 563. https://link.springer.com/article/10.1134/S1063772916040107. Originally published in the Russian Astronomicheskii Zhurnal 93 (6), 546; also in arXiv: https://arxiv.org/pdf/1607.02596.pdf; this paper was also cited with some formation time estimations by Lerner, 2022. Observations of Large-Scale Structures Contradict the Predictions of the Big Bang Hypothesis But Confirm Plasma Theory. https://www.lppfusion.com/storage/Structure-2022-.pdf). The Shirakov group discovered that the structures sampled in their pencil-beam survey showed massive departures from the homogeneity curve, complete with deficit and excess densities of galaxies:

What these pencil surveys imply is that there are structures so vast that they are astoundingly ~/≥ 3 Gpc in size or more (~/≥ 9.8 Gly). This is staggeringly beyond the HBBC ΛCDM model's assumptions of homogeneity. In his comments upon Shirakov et al. (2016)'s Figure 2a above left, dissident plasma cosmologist Eric Lerner (2022) wrote the following description of what we observe here, including that these distances are ΛCDM model dependent.

Musings on gigantic structures from a non-paradigmatic & paradigmatic stance. If these giant structures are gravitationally-bound (as they would be in the supposedly homogenous, isotrophic Big Bang world, compounding the "dark matter" ad hoc problem) rather than coming apart from their multiple origin points (as they would be in the modified cyclic or Quasi Steady State universe with negative, scalar C-field activation in the presence of pre-existing matter gravitational concentrations, or some other theoretical scenario), then they should require billions of years longer than the 1/H₀ supposed age (~13.8 Ga) of the Big Bang cosmos to form. Under even gravitationally-bound, viriality assumptions (see discussion in the forthcoming chapter IX on "Vast jets, and galactic ejection phenomena"), these may be direct empirical evidences in their own right that we live in a Universe far older and by implication vaster than the HBBC scenarios.

Conversely, despite the multi-featured nature of the accumulating data, Ethan Segal, in a pro-paradigmatic op-ed in January 2024, questioned the growing published claims that such HBBC-verboten large structures as the "Big Ring" or the "Giant Arc" actually exist out there, and are not mere visualized apparent patterns. He also critiques the Hercules-Corona Borealis Great Wall, the Giant GRB Ring, the Huge-LQG, the U1.11 LQG, and the Clowes-Campusano LQG: All "ranging in size from ~2 to ~10 billion light years," he adds. The only large structure he does not question is the HBBC-compliant CfA2 Great Wall then reported to be 600 x 250 x 30 million light years in size (Geller & Huchra, 1989). Although question-raising in its own right, this <1 Gly large structure was comfortable enough so that Michael Riordan & David Schramm could publish their paradigmatic 1991 volume, Shadows of Creation: Dark Matter and the Structure of the Universe. New York, NY: W. H. Freeman (link), which popularized the 'dark matter' web scaffolding for ordinary matter in the HBBC. Segal cites the Malmquist bias (an astronomical bias-in-detection of intrinsically-bright objects [link], a bias which also illustrates the selective HBBC-inspired interest in certain bright objects and not in others in cosmology, as is evident in certain publications cited in chapter V for instance) as a possible source of such 'structures.' He argues that there is "little-to-no evidence" and these patterns are like extra-galactic 'asterisms' mistaken by statistics for an actual star cluster, like the nearby asterism (~5,000 ly), Brocchi's 'cluster':

Segal op-ed's citation of various figures:

(link). In citing this artist representation, Segal avers that since galaxies (in 'cosmic filaments' whatever that means in model-dependent and model-independent ways) are surrounded by matter in neutral and ionized, the absorption spectra show the density and temperature not only of the intergalactic media around those galaxies, but also around the intervening galaxies, and in our own galaxy, so therefore such absorption spectra (as in the Mg-absorption of the 'giant arc' and 'big ring') are biased / imperfect indicators of underlying mass distribution, which he asserts paradigmatically includes 'dark matter.' Aside from the fact that the absorption features likely have their own spectral redshifts, he does not mention that the 'dark matter' existence is an assumption required by the deeper assumption of viriality in the HBBC ΛCDM. So the claims of beyond ΛCDM-allowed large structures existence should not simply be dismissed on such model-based grounds.

Figure adapted from Tegmark et al. 2003. The 3D power spectrum of galaxies from the SDSS. https://arxiv.org/abs/astro-ph/0310725; 2004. The three-dimensional power spectrum of galaxies from the Sloan Digital Sky Survey. ApJ 606 (2), 702. https://doi.org/10.1086/382125. (link). The op-ed cites the redshift-space 'fingers of god' (FOG) distortions (or phenomena) as artifacts which had to be removed from the SDSS galaxy sample, assuming the effect was entirely caused by galaxy proper motions in an HBBC cosmos. Actually, there are reasons to think that there are data of cosmological model-testing significance in the so-called 'fingers of god' phenomena, as discussed below.

(cit. link). Segal's op-ed also slams the claims about large structure derived from QSOs (which he claims are the result of non-merging galaxies) and from transient Gamma Ray Bursters (GRBs), such as GRB170817A pictured above, in part because GRBs are found in ordinary galaxies caused by neutron star collisions resulting in kilonovae, which can be juxtaposed, and therefore don't necessarily represent large structure markers. However, if the large structures with mostly ordinary galaxies exist, one would expect that GRBs would illuminate these in 'Christmas tree' style. His argument here seems particularly weak.

Brocchi's 'cluster' which is really an asterism: (op-ed annotated link citing link). As an example of his claims about artifactual juxtapositions of QSOs or GRBs, Segal cites the asterism, which statistically (without other information) was thought to be a bona fide star cluster. Of course, the authors he critiqued, while using statistics to buttress their claims of detecting large structures, also cited data beyond mere juxtaposition.

Segal's op-ed also expressed his peeve about the UCLan issuing a press release (link) before the Lopez et al. (2024) paper was released. His annoyance and pique seems unnecessary given that the university wished to highlight and generate interest in the work of their doctoral student Alexia Lopez and her her advisor, so that when the paper was released, a discussion could begin. One hopes that the controversy is not what causes annoyance.   

Gigantic Voids as inverse structures. Concomitant with an extremely interesting feature of large cosmic structure is the existence and nature of large-scale and even giant cosmic voids found in intergalactic space:

Although the newly-discovered galaxy cluster, VVVGCl-B J181435-381432, at z = 0.225 ± 0.014, in our galactic ZOA, is modest compared to the massive and vast extragalactic structures we've been considering, it is another glimpse to where we've not seen before, a continuation of the quest behind human cosmology-making, to peer where no one has peered before.

Now, we can direct ourselves back to the vast 'voids' observed in the Universe.

In fact, we now realize that we live in a "local void" out to about ~200 Mpc (~652 Mly). Wong et al. (2022. The Local Hole: A galaxy under-density covering 90% of sky to ≈ 200 Mpc. MNRAS 511 (4), 5742. https://doi.org/10.48550/arXiv.2107.08505, version 5 in arXiv: https://doi.org/10.1093/mnras/stac396) have shown that in this local hole, there is an under-density of galaxies at about ~22% by two different estimates.

This is in tension with the homogeneity predictions of the ΛCDM cosmology by about ≈ 3𝜎. Since the Local Hole is out to about 200 Mpc, it is worth observing that the diameter of the Local Hole is ~400 Mpc (~1.31 Gly), again above the predicted ΛCDM upper limit.

These giant voids are like spherical like cosmic 'soap bubbles' with galaxies on their surfaces. These intergalactic voids have a wide range of diameters. Centered about 75 million light-years from us, the Local Void centered is about 150 million light-years across, about half the diameter of another cosmic void. Another cosmic void discovered in 1981 is the Boötes Void or the 'Great Void' which is about 300 million light-years across, and it's center at z = 0.052 or about 700 million light-years away (Richard Powell, NASA; https://www.flickr.com/photos/nasablueshift/9402300439/):

The 150 million light-year Local Void (NASA) with faint dwarf galaxy ESO 461-36. Credit: UDS/CNRS (https://asd.gsfc.nasa.gov/blueshift/index.php/2013/07/30/jasons-blog-next-stop-voids/).

The 250-330 million light-year in diameter 'Great Void' in Boötes, with the visible bodies being in front of the cosmic void (https://asd.gsfc.nasa.gov/blueshift/index.php/2013/07/30/jasons-blog-next-stop-voids/; Image: Richard Powell, Atlas of the Universe: http://www.atlasoftheuniverse.com/).

Canes Venatici, a constellation with the 'Giant Void' is in angular proximity to the 'Great Void' in the constellation of the Boötes the Herdsman:

Canes Venatici (above pictured in the Hevelius' Atlas Coelestis, 1690; note the inverted "god's eye view" of the celestial cartographer, as if viewing the constellations from outside the 'celestial sphere') contains the Giant Void, 1-1.3 billion light-years in diameter. It is in angular proximity to the constellation Boötes, which includes the smaller 250-330 million light-year 'Great Void.'

The 'Giant Void' or Canes Venatici supervoid

The 'Giant Void' of Canes Venatici (http://tothelandofdreams.blogspot.com/2016/07/canes-venatici.html).

It is interesting that no evidence of galactic streaming around the 'Giant Void' as predicted by BB-associated models with 'dark matter' has been detected (Kopylov & Kopylova, 2002; https://www.aanda.org/component/article?access=bibcode&bibcode=2002A%252526A...382..389KPDF).

Large-scale structure & the CMB. Radio astronomers (NRAO Very Large Array) a few years ago discovered a large nearly billion light-year in diameter cosmic void revealed through a paucity of radio sources in a 1 degree region of the sky, which also not surprisingly (if one questions the Big Bang) corresponds with a temperature dip in the CMB of the WMAP data. (Rudnick et al. 2007; https://arxiv.org/abs/0704.0908).

(Rudnick et al. 2007) (Szapudi et al. 2015)

According to the hot Big Bang cosmologies, the CMB fluctuations are supposed to represent primordial fluctuations in the very radiation background which is supposed to be the clinching data set / primordial 'dying echo' for the Big Bang & specifically not something as 'mundane' as variations because of the large scale structure of matter.    A series of papers attempted to come to terms with the possible correlation between a large cosmic galactic void near the last surface of scattering in the direction of the sky and the CMB 'cold spot.' The danger to the Big Bang cosmology is that one might recognize the CMB temperature fluctuations to be linked causally to the surrounding large-scale structure of the Universe—the most parsimonious null hypothesis. However, everything was done to avoid the obvious. Appeal was made for corrections based on an integrated Sachs-Wolfe (ISW) effect, which assumes that the CMB is cosmological and that correction must be made for intervening and local distribution of matter since the last cosmic Thomson scattering of the CMB photons. 1967: Sachs & Wolfe, assuming simple Friedman-Lemaitre models, the CMB as cosmological, non-curved (k = 0) space-time, and a q0 = +1/2 (consistent with data at the time, although we know today that q0 = ~ -1, as long predicted by the CSSC!), calculated the angular variations in the CMB arising from "density fluctuations, rotational perturbations, and gravitational waves" expected in these carefully chosen FL models (http://adsabs.harvard.edu/abs/1967ApJ...147...73S). 2006: Inoue & Silks argued that local voids could cause large-angle CMB anomalies by using an adjusted ISW effect (between an "ordinary" and "late-time" effect to accommodate q0 = ~ -1) in order to be consistent with the ΛCDM (accelerating cold dark matter version of the Big Bang) model (https://arxiv.org/abs/astro-ph/0602478v2). 2007: Rudnick et al. find a correspondence between the CMB 'cold spot' and a drop / void in the radio source count (https://arxiv.org/abs/0704.0908). 2007 (-2008, 2011, 2018): Smith* & Huterer, in a paper curiously remaining in the preprint process between 2007 and its final publication in January of 2018, worked very hard using various a posteriori selection cuts, flux smoothing procedures, and statistical re-analyses to show that there is no corresponding dip in radio sources associated with the CMB 'cold spot' and surprisingly frankly acknowledged their motivating concern: "Such matching cold spots would be difficult if not impossible to explain in the standard ΛCDM cosmological model." (Please just make it go away!!). Not surprisingly, data are sparse in their paper. In their conclusion, they wrote: "Despite the null result of this paper, one should not be disheartened. More detailed observation of the cold spot region in galaxy surveys will likely improve confidence about the existence of any over/underdensity or lack thereof" (https://arxiv.org/abs/0805.2751). Although delayed until 2018, this paper curiously makes no reference to the Planck 2013 re-mapping of the CMB.  2015: In a data-rich paper Szapudi et al. showed through very careful z-binned data and analysis that there is indeed a galactic supervoid about 1.8 billion light-years across coincident with the CMB 'cold spot.' The group suggested further research but were very careful to include, "Such a supervoid, constituting at least a ≃ 3.3σ fluctuation in a Gaussian distribution of the ΛCDM model, is a plausible cause for the Cold Spot" (https://arxiv.org/abs/1405.1566). 2016: Nadathur & Crittendon applied "a matched-filter approach" to detect an ISW "imprint of cosmic superstructures" (https://arxiv.org/abs/1608.08638). Throughout and especially lately, some ΛCDM adherents have also sought for exotic explanations for the troublesome 'cold spot' through appeals to possible parallel universe, such as a quantum entanglement of our universe with another during the 'inflationary epoch.'     Integrated ISW effect in degrees K averaged among 50 known cosmic voids (Granett, Neyrinck, & Szapudi, 2008; https://arxiv.org/abs/0805.3695; image: https://en.wikipedia.org/wiki/CMB_cold_spot). WMAP image of the CMB with the 'cold spot' indicated. (https://apod.nasa.gov/apod/ap110321.html)

*Ironically, Smith is affiliated with the Institute of Astronomy at Cambridge, originally established as the Institute for Theoretical Astronomy in a more open-minded frame by Sir Fred Hoyle.

In the popular write-up about the Szapudi et al. (2015) paper, Vox stated that "fewer galaxies" are only "a partial explanation" for the 'cold spot' in the CMB. In their publicity figure (below) from the ESA Planck Collaboration, "corrections" and accounting for astronomical structures on the CMB is blindingly obvious, even structures as local as the Andromeda Galaxy and our Moon. The CMB would be taken by scientists for what it is phenomenologically, a straightforward scattering and thermalization of radiation by matter from local and large-scale astronomical structures distributed throughout the Universe, if it were not supposed to continue to play the role of the master linchpin and Gaussian remnant of a "primordial fireball" in the modified ΛCDM Big Bang cosmology. Instead the CMB is an endless theoretical 'thorn in the flesh' of the Big Bang establishment, requiring endless specialized corrections, parameter adjustments, filtering, smoothing, and scrubbing of it's data. The ancient Pythogoreans trying to conceal the 'appalling' existence of irrational and transcendental numbers would have been proud, as would any of the pious protectors and defenders of the Old Ptolemaic system against the Copernican Revolution.

The empirical data indicate strongly that the inhomogeneities and anisotropies of the CMB are determined in a major way by intervening large scale structures in the Universe, rather than some supposed primordial conditions at ~340,000 years post-Bang.

Image: ESA Planck Collaboration (https://www.vox.com/2015/4/21/8461329/supervoid-cold-spot)

Peculiar non-Hubble flows of galaxies, such as the galaxies (including our own falling toward the Great Attractor centered in Centaurus) and the likely effects of intervening galactic groups have never been accurately assessed for their effect on the CMB (https://giphy.com/gifs/galaxy-Znl8ETAk6iY9i, cf. https://imgur.com/gallery/1ioCq; http://www.atnf.csiro.au/people/mcalabre/animations/index.html).

We develop in greater detail issues related to questions about the CMB in our section, "The Cosmic Microwave Background (CMB) radiation: From Where and Whence?"

On cosmic voids and supervoids, an interesting study from Argentina's National University of about 245 cosmic voids discovered through the Sloan Digital Sky Surveys (http://www.sdss.org/surveys/) that these cosmic voids were changing in size and had specific velocities 300-400 km/sec faster than indicated by red-shifts of the galaxies surrounding them (Lambas et al. 2015, https://arxiv.org/abs/1510.00712, Lambas et al. 2016. The sparkling Universe: the coherent motions of cosmic voids. MNRAS Letters, 455 (1), L99. https://doi.org/10.1093/mnrasl/slv151. cf. discussion by Cowen, Nature 2015, https://www.nature.com/news/vast-cosmic-voids-merge-like-soap-bubbles-1.18583; http://cosmologyscience.com/cosblog/gigantic-voids-are-expanding-and-shrinking/#more-6920). Attempts to explain these goings on within Big Bang cosmology require the conjuring up of further ad hoc adjustments appealing to "dark matter" and "dark energy" mechanisms. If one lets the Big Bang go, much less ad hoc and more organic, empirical models of our Universe are possible.

Furthermore, large-scale intergalactic structures of intergalactic neutral hydrogen gas clouds are found intervening between Earth and a distant quasar at a red-shift of z = 3.62, revealed by spectral forest of emission and absorption lines. Naturally arising in the Classic Steady State Cosmology (CSSC) such intergalactic hydrogen is predicted by negative scalar c-field hadron creation mechanism, whether in the classic or quasi Steady State cosmologies. And of course, other cosmologies are possible models too.

Top: A typical high-resolution spectrum of a quasar Q1422+2309 at redshift z = 3.62. At the spectral shorter wavelengths of the redshifted Lyman emission line at 1216(1 + z) Angstroms, the spectrum shows a 'forest' of absorption lines of different strength produced by intervening neutral hydrogen gas (not consistent with electrical plasma type models) along the line-of-sight from the quasar to the Earth. Bottom: Hydrodynamical simulations reproduce a segment of the observed absorption spectra, corresponding to intervening. Middle panel: An example of the gas distribution in a simulated, highly-parameter-adjusted ΛCDM model (Springel et al. 2006).

Another extremely high redshift (pre-JWST) quasar (z = 6.53) with its Lyman-α forest of emission and absorption spectral lines has also been spotted in the accumulating DESI survey (2022). Notice that this quasar which is thought to be close to 13 Gly away is found in a far distant field of galaxies with a full range of galactic stellar ages, as would be expected in an older, vaster Universe.

Again an HBBC model-dependent interpretation is put forward in the caption:

(https://newscenter.lbl.gov/2022/01/13/dark-energy-spectroscopic-instrument-desi-creates-largest-3d-map-of-the-cosmos/).

Empirical thought: Of course none of this ad hoc curve-fitting is required if one does not insist on the young Big Bang model but allows the Universe to be as old and as vast as it is increasingly, empirically shown to be, and modeled through a more empirically-based theoretical framework.

Combined large-structure galactic redshift surveys across different sections of the skies compared with the Millennium simulation (Springel et al. 2006). 

Thus with this study and others, the emerging data strongly suggest that both the homogeneity and the isotropy assumptions of the Cosmological Principle (CP) as needed for the FLRW metric of the HBBC ΛCDM model of cosmology are deeply violated by those very accumulating data. We expect that the coming research will reveal further such violations as the prevailing New Ptolemaic paradigm continues to face its Kuhnian crisis. Any paradigmatic theory still worth its scientific salt should be making ongoing successful predictions about the World. The standard HBBC ΛCDM concordance cosmology is no longer making successful predictions, and continuously requires various and looming epicycles to even attempt to keep up with the growing data, and to fail at doing so. A new fruitful, predictive cosmology is needed. We turn next to a 102 page review of the situation, which asks many of the right questions.


Are the homogeneity and isotropy assumptions behind the HBBC ΛCDM model even met? Is the Cosmological Principle (CP) foundation of modern standard cosmology sound? In 2022, a collaboration, including Alexia Lopez, submitted a massive review paper on the issue of observational violations of the Cosmological Principle (CP) in the predicted spacetime metric of the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies and whether the anomalies have accumulated to the point where the FLRW cosmologies in their currently-favored ΛCDM model has been outgrown by cosmology: Aluri, P. K. et al. 2022 (arXiv: https://arxiv.org/abs/2207.05765, four versions). 2023. Is the observable Universe consistent with the Cosmological Principle? Class. Quantum Grav. 40, 094001. 103 pp. https://doi.org/10.1088/1361-6382/acbefc. We cite the reviewers' state of the Cosmological Principle, with some added clarification: "The cosmological principle (CP) is a working assumption in modern cosmology that can be simply stated as the Universe is (statistically) isotropic and homogeneous at suitably large scales" (emphasis theirs), to which we qualify for clarity that statistically means what is observed at representative scale for any observer in the Universe, meaning our vantage point is not special but typical.

How important are the assumptions of homogeneity and isotropy at representative scale in the FLRW cosmologies? The reviewers point out the criticality of these assumptions which are required to solve the equations of general relativity, and "once the FLRW symmetries are imposed and the energy-momentum tensor associated with a homogeneous and isotropic cosmic perfect fluid specified, the Friedmann equations reduce to a first order ordinary differential equation with a unique integration constant, namely the Hubble constant H₀. As a result, within the FLRW paradigm, H₀ is a universal constant parameter in any FLRW cosmological model." That is, these assumptions which comprise the CP are indispensable in FLRW HBB cosmology. One of the Bianchi-type cosmoses would be one where the homogeneity assumption is met but not the isotropy assumption, and no one is yet stating that we are compelled by the data to postulate such a cosmic model.

Since in the FLRW model, the H₀ is a universal constant in a spherical time-space slice homogenous-isotropic cosmos, the 'Hubble tension' is the beginning of sorrows for standard cosmology on the issue of the CP assumption (which we have reviewed in ch. VII. Unexpected galactic Redshifts), and furthermore, which the JWST data has not alleviated but actually aggravated for the standard model. The reviewers emphatically state, "the discrepancy between local determinations (measurements) based on Cepheids and Type Ia supernovae (SNe) (H₀ = (73.04 ± 1.04) kms⁻¹ / Mpc) and Planck’s analysis of the CMB based on the ΛCDM model (H₀ = (67.36 ± 0.54) km s⁻¹ / Mpc) has now reached a discrepancy of 5σ." What they don't state is that this result calls into question the very central notion of the primordiality of the CMB, a sacred cow in standard HBBC cosmology. They go on to state on the question of the isotrophy assumption that "Later we will argue that this actually extends to orientations on the sky, so the Hubble tension may be a three-dimensional problem and not a one-dimensional (redshift) problem, as is routinely assumed." (emphasis theirs).

This review highlighted key ares for testing these cosmological assumptions:

• Homogeneity scale (the scale at which large structures can form, which we have been reviewing above) according to the flat ΛCDM model under N-body simulations under Friedmann-Lemaître-Robertson-Walker (FLRW) metric has a lower bound of 60–80 h⁻¹ Mpc and an upper bound on the homogeneity scale of 260 h⁻¹ Mpc. Even as early 1989, the Geller-Huchra 'the Great Wall' with its size at 600 X 250 X 30 million light years in size or ~200 Mpc, i.e., ~650 Mly. This upper bound has long already been violated by the Sloan Great Wall galaxy structure with a scale of ~420 Mpc (see above), let alone the original Clowes-Campusano LQG (large quasar group) at ~2 Gly in length and ~1 Gly in width, the two QSO clusters at 350-400 Mpc (~1.14 - ~1.3 Gly), the SDSS DR7QSO group, the largest know of the LQGs (large quasar groups), with enormous dimensions of the Huge Large Quasar Group (Huge-LQG) at 1.24 Gpc (~4.04 Gly) long by 640 Mpc (~2.1 Gly) and 370 Mpc (~1.2 Gly), the South Pole Wall at ~400 Mpc or ~1.31 Gly, or the possibility that the Shapley Wall, the Great Attractor, South Pole Wall, the Perseus-Pisces cluster and Lanakea are all part of one giant structure. Then there's Giant Arc at ~3.3 Gly  across, and now the Giant Ring / Corkscrew at ~1.3 Gly and a circumference of ~4 Gly, which may be actually both facets of an even more gigantic structure at about ~9.2 Gly distant! And that's not all, there is the gigantic ring-like structure of gamma ray bursters (GRBs) at about 1720 Mpc (~5.61 Gly) in size. Above we also covered the pencil surveys which revealed gigantic (running out of size superlatives) repeating structures at ~/≥ 3 Gpc in size or more (~/≥ 9.8 Gly), and of course the giant voids and chasms of low galaxy occurrence which even affect the CMB, inducing giant cold spots in the supposed primordial surface of last scattering at ~380 years post-Big Bang. These are all increasingly astounding violations of FLRW expected homogeneity.

A few of the large-scale structure violations of homogeneity scale reviewed in the following figures from the Aluri et al. (2022; 2023) review paper:

And these cited examples do not include all the even more amazing homogeneity violations we have explored and summarized above. However, the Aluri et al. (2023) paper, figure 4 also raises the issue of the isotropy assumptions of the FLRW. The great astronomer Vera Rubin discerned (as cited in the review) regarding the 1989 discovery in CfA data of 'the Great Wall': "It certainly has convinced me that we’re not living in a homogeneous, isotropic [Universe]. I mean these things that I really suspected in the back of my mind, I can now say publicly. I’m not sure the Robertson-Walker Universe exists." —Vera Rubin on the 1989 discovery of the CfA Great Wall (emphasis added). Her praiseworthy honesty is refreshing. Next we turn to the troubling prospect of an anisotropic cosmos, as hinted in their Fig. 4 and detailed in some of the studies we have cited above.

• On the question of violations of FLRW ΛCDM expected isotropy and of the Cosmological Principle (CP), the reviewers in keeping with the FLRW ΛCDM paradigm have divided their survey of challenging data in terms of spherical time-slices required in an FLRW metric solution between (a) the putative early FLRW anomalies (such as anisotropic cosmological parameters, topological anomalies in the CMB, parity violation, &c.) and (b) putative late FLRW anomalies (like galaxy cluster anisotropies, anomalous bulk flows of galaxies, radio, QSO, and SNe Ia dipole anisotropies, &c.). As can be seen from the figures, there are multiple anisotropic anomalies in violation of the CP in the FLRW ΛCDM paradigm in their following Figure 1 and its corresponding Table 1 where they 'count the ways' in which isotropy is violated.
  

The sheer number and variety of anomalous anisotropies within the FLRW metric paradigm is astounding, both in putative early and late FLRW anomalies. This naturally suggests that it's indeed time to reexamine the cosmological models on offer, and search perhaps for new ones. In the reviewers discussion of the various anomalies, they suggest that there are tensions with the FLRW, which may make it less precise than desirable and some anomalies remain unexplained. They hope for further surveys of the data. We may return to more of these results later. Suffice for now to show that tensions exist and that paradigms need to be tested further at the least.

At this juncture, we will be augmenting our discussion with the ballooning new JWST data on galaxies with even higher z values, which are further illustrative of the same trends.

Within this next section, we turn in brief to the issue of the connection between galactic morphology and systematic effects in redshift measurements, and to a possible explanation for the 'fingers of god' effect.

The 'fingers of god' effect—A systematic but morphological-selective bias superimposed on the overall Hubble relation. Also observable in the images above and below is the so-called 'fingers of god' phenomena where galactic redshifts are plotted as a function of distance (Hubble relation) the computations yield an apparent situation where large structures often point straight at earth! This peculiar phenomenon has been interpreted in the orthodox HBBC explanation as a bias created by the proper (nonradial) motions within the galaxy cluster among the various galaxies within the cluster. But this does not explain why there is a bias in the redshift-related direction, and as we shall see of galaxy classification type, creating the apparent but spurious effect of trailing structures 'pointing' back to the observer on earth.

'Fingers of god' phenomenon observed in this figure and the two preceding figures (http://electric-cosmos.org/arp.htm).

The data however indicate that on the average there seems to be a component of the redshifts which are intrinsic to the galaxy morphology type: Elliptical (E0-E7), spiral (S0_1-3, Sa, Sb, Sc), and barred spiral (SB0_1-3, SBa, SBb, SBc). The normal, more 'relaxed' spirals having the lowest average redshift within a cluster, while the more 'disturbed,' higher energy elliptical and barred spiral galaxies have higher average redshifts. (This anomalous intrinsic, excess redshift connected with smaller, more energetic galaxies (AGNs) when interpreted as part of the Hubble shift-distance relation, yield the purely artifactual 'fingers of god' effect. This odd artefactuality disappears when one recognizes the existence of an intrinsic redshift component, which cannot be explained in the HBBC.

The large effect is also visible in the Proust et al. (2006) survey.

Along the x-axis, one sees the redshift values as if they were strictly Doppler, up to 60,000 km/s (http://www.haltonarp.com/articles/fingers_of_god_in_an_expanding_universe/illustrations/cone_diagram.jpg).

Even in the recent (2022) emerging DESI 3D slice survey results (>5 Gly / 1500 Mpc), the huge structures and the 'fingers of god' phenomena are manifest popping into and out of view upon observation of this animate cosmographic map:

Even the caption on this heavily processed animated .gif of the data accentuates the HBBC model-dependent interpretation of this cosmographic map, making no mention of the redshift peculiarities which generate the visible 'fingers of god' effect, caused by the added intrinsic redshift component, especially noticable under 500 Mpc:

 

(https://newscenter.lbl.gov/2022/01/13/dark-energy-spectroscopic-instrument-desi-creates-largest-3d-map-of-the-cosmos/).

Such intrinsic red-shift effects overlaid as they are on the general Hubble relation are what are expected and predicted in quasi Steady State cosmologies, where some fraction of the z-values result from negative scalar c-field activations around heavy gravitational centers resulting in novel baryonic matter ejection understood within a Machian gravity framework, such as proposed by Hoyle & Narlikar (1964). These features find no explanation in the standard, or adjusted HBB cosmologies. Later, we consider direct astronomical data of such possible predicted new baryonic ejection events.

Hubble Galaxy Classification 'Tuning Fork' diagram
Implications of classifications of galactic evolution for cosmological model tests

Ancient morphologically-mature spiral starburst galaxy

Unexpectedly, from the standpoint of the HBBC paradigm, essentially the same spread of younger bluish and older reddish galaxies of differing morphologies were found by Lee et al. (2013) by z ~ 2. The implications for competing cosmologies are evident (see link). Again these data fit the Steady State type or plasma cosmologies which predict such an ongoing diverse distribution of galactic ages at vast distances in an infinite, or indefinitely old Universe, as discussed previously.

In one of the deepest views prior to developments from the JWST, galaxies of all different morphologies, various stellar spectral ages, going back across billions of light-years out to ~13.1 Gly have been assayed in the Hubble Ultra Deep Field (Rafelski et al. 2015. UVUDF: Ultraviolet through Near-Infrared catalog and photometric redshifts of galaxies in the Hubble Ultra Deep Field. AJ 150 (1), 31. https://iopscience.iop.org/article/10.1088/0004-6256/150/1/31).

Excerpt of the Hubble Ultra Deep Field view with estimated redshift distances (Rafelski et al. 2015).

Look back time across billions of light years (Ibid.).

Angular scale of the HUDF within 1 degree of the sky (Ibid.).

HUDF near Eridanus (Ibid.).

Eridanus (the River), 'Bayer's drawings' (Bayer, 1661 ed.): https://skytonight.org/eri.

As seen near the constellation Eridanus (the River), also featured color-inverted from Johannes Bayer, Uranometria (1661 edition).

Pie diagram of redshift vs. sky angle for all galaxies listed as Virgo Cluster members in Sandage & Tamman's Revised Shapley Ames Catalog
(Image used by kind permission from Arp, 1998).

Virgo Cluster: Galaxy morphological type differences in redshift (Image used by kind permission from Arp, 1998).

Virgo Cluster.

The Local Cluster of galaxies (Image used by kind permission from Arp, 1998).

Abell Cluster 262: Galaxies brighter than 15th magnitude (Image used by kind permission from Arp, 1998).

Also, clusters with galaxy distributions in different stages of morphological development (i.e., different ages! Image used by kind permission from Arp, 1998).

(Image used by kind permission from Arp, 1998).

(www.haltonarp.org).

Dilation Redshift scatter (Joseph, 2010b).

Excess redshifts found in active nuclei Seyfert galaxies represented by triangles.
(Image used by kind permission from Arp, 1998).

Excess QSO redshifts (Joseph, 2010b).

In 2003, D. G. Russell released a paper, Intrinsic redshifts in normal spiral galaxies. https://arxiv.org/abs/astro-ph/0310284, a paper which was released in updated form: (2004 arXiv: https://arxiv.org/abs/astro-ph/0408348), and published in 2005: Evidence for intrinsic redshifts in normal spiral galaxies. Astrophys Space Sci 298, 577. https://doi.org/10.1007/s10509-005-2317-x. Russell summarized data showing that even ordinary spiral galaxies have some currently unexplained excess redshift component, above the Hubble constant redshift-distance relation expectations. In his 2003 manuscript, Russell had diagrams to show this, including some intrinsic additional redshift data seemingly dependent in part on morphology: https://arxiv.org/ftp/astro-ph/papers/0310/0310284.pdf. We turn now to these data as encapsulated by reference to his 2004 tables and figures. By way of introduction, Russell follows up on the many published references to non-Hubble relation / intrinsic and discordant redshifts between apparently associated / ejected objects of different redshifts (covered in introductory form in this chapter VI, as well as in greater detail with other papers cited in chapters VII, VIII, IX, X, and XII in this history—some of these chapters published in draft and others yet to be published).

Russell makes use of the Tully-Fisher Relation (TFR: Tully, R. B. & Fisher, J. R. 1977. A new method of determining distances to galaxies. A&A 54 (3), 661-673. https://articles.adsabs.harvard.edu/full/1977A%26A....54..661T; cf. on TFR in 'dark matter' HBBC: Combs, F. 2009. COMMENTARY ON: TULLY R. B. AND FISHER J. R., 1977, A&A, 54, 661: From distances to galaxy evolution and the dark matter problem. A&A 500 (1), 119-120. https://doi.org/10.1051/0004-6361/200912152) as an independent distance check to be compared with his working value of the Hubble constant as H₀ = 72 km s^-1 Mpc^-1. The TF relation (1977): "We propose that for spiral galaxies there is a good correlation between the global neutral hydrogen line [HI] profile widt, a distance-independent observable, and the absolute magnitude [M] (or diameter)." The hypothesis being tested by Russell is what we have called the Ambartsumian-Arp cosmogony (cf. Vorontsev-Vely'aminoff, probably more accurately called the AV-VA model, which we will discuss at length :), a model of galactic evolution: "...some quasars may be ejected from active Seyfert galaxies as high redshift objects that evolve to lower redshifts as they age." Russell explains, "In this model the intrinsic redshift component is related to the age of a galaxy such that younger galaxies have a larger intrinsic redshift component than older galaxies," (cf. cit. Narlikar, J. & Arp, H. 1993. Flat spacetime cosmology: A unified framework for extragalactic redshifts. ApJ 405, 51. https://adsabs.harvard.edu/full/1993ApJ...405...51N) while Bell (2002a; 2002b ) proposed an intrinsic redshift component imposed on the Hubble relation.

Narlikar's theoretical 'aiding and abetting' of the AV-VA cosmogony, to parody Gamow's spousal poem on the Hoyle-Ryle controversy (see forthcoming chapter III).

Prof. J. V. Narlikar wrote to Indian president seeking 'reassuring action' on growing intolerance (link). In summary, the Ambartsumian Vorontsev-Vel'yaminov Arp (AV-VA) cosmogony: Involves the following elements: Compact high z objects like QSOs / BSOs are ejected from the cores of AGNs with (Machian) high intrinsic redshifts As they stream away from the semi-major axis of the AGN, they gradually lose their high intrinsic redshifts through Machian interactions Steadily until they fall back toward the parent galaxy with redshifts only slightly elevated above the & falling back toward the ordinary Hubble flow based on H0 values. Halton Arp has called this 'an empirical cosmogony' because it arises from direct anomalous observations, and also seeks explanation within a variation of the (Machian) Hoyle-Narlikar theory (1964ff, 1966, &c.). (Figures opposite used by kind personal communication permission of the late Halton Arp, but will be discussed in the context of their original appearances in the peer-reviewed references; cf. Arp, 1968 volume in the homepage Select Bibliography).

We will return to this AV-VA cosmogony as a recurring test-case hypothesis in the following chapters cited above. As Russell framed it, his paper was meant to test: "If galaxies and quasars do contain a component of intrinsic redshift then the implications for cosmological models are significant. It is therefore important to establish whether or not the redshift anomalies are real by direct means." This is what Russell set about doing, including going through 6 alternative hypotheses (Ibid., pp. 17-19). We'll show his data and let the reader explore more, where the options were explored, including elimination of the Malmquist bias, &c. (See Methods):

Russell (2004) data.

Table VII cont.

Russell (2004) Appendix figures.

 

Russell (2004) concludes conservatively the following: "The results of this study support previous claims for large redshift anomalies in normal spiral galaxies (Arp 1988, 1990, 1994; Russell 2002). It was found that within large clusters there is a tendency for late type Sbc/Sc spirals to have significantly larger mean redshifts than early type Sa/Sb spirals. The most extreme case is the ScI’s in Virgo which have a mean redshift ~1500 km s^-1 greater than the mean redshift of the large Sab/Sb spirals in Virgo. The excess of Sbc/Sc spirals relative to Sab/Sb spirals in Pisces and Serpens was +552 km s^-1 and +1604 km s^-1 respectively." Moreover, Russell continues, "It is not clear what phenomenon can explain the redshift anomalies that the empirical evidence of this study indicate exist. The following possibilities are considered:" Although the following are quite dated given the literature cited then, they are worth repeating to illustrated the undone homework which could be done with far superior data now, >2 decades hence. (The emphasis is Russell's).

• "(1) Morphological Density Relation.
• (2) Value of the Hubble Constant. 
• (3) Large Scale Flows. 
• (4) Gravitational Redshifting. 
• (5) Cepheid Calibration. [Comment: Of course we now have JWST on top of HST Cepheid calibration showing that JWST provides no relief for the 'Hubble tension' from Cepheid variables].
• (6) Real Peculiar Motions. Russell continues, "However, there is no precedent for such large peculiar motions in galaxy clusters or field galaxies. In addition, large peculiar motions cannot explain the systematic excess redshift of the ScI group galaxies as there should be large deficits of redshifts for approaching galaxies." [Comment: If viriality is violated as Ambartsumian first proposed in the 1950s, then this is not a surprise. Perhaps a generalziation of the 'law of conservation' of baryon number is required as Ambartsumian proposed, and as the CSSC stated in another context, mid-last century].
  

Finding these wanting, Russell (2004) states, "The large redshift anomalies identified in this analysis are a challenge to explain in standard views. Given that conventional explanations are insufficient, there is reason for considering more exotic alternative explanations." Perhaps modified Newtonian gravitation or a model CGC (Bakhos, 2022) would help? In his concluding paragraph, Russell states, "The results of this analysis strongly suggest that large redshift anomalies exist in normal galaxies which are most likely non-doppler (intrinsic) in nature. While the exact mechanism for intrinsic redshifts is necessarily speculative at this time, the empirical evidence is consistent with the intrinsic component of redshifts being in discrete amounts and age related such that younger objects have a larger component of intrinsic redshift than older objects at the same distance" (Russell, 2004).

One can only wonder why these anomalous data from the early part of this millennium were not and have not been taken into proper account in the question of the 'Hubble tension' discussed and reviewed in the literature since then and cited in our next chapter VII, Unexpected galactic redshifts?

Since 2017 in the SDSS data, we can differentiate two actual types of Seyfert AGN galaxies morphologically (Seyfert 1s are more likely in bulge-dominant galaxies and Seyfert 2s are more likely in spirals) rather than in a simple unification model of Seyferts (which held the differences to be based on the orientation of the galaxy from which the Seyfert AGN is viewed telescopically): Chen, Y. C. & Hwang, C. Y. 2017. Morphology of Seyfert galaxies. arXiv (v2): https://arxiv.org/abs/1707.08806. Astrophys Space Sci 362, 230. https://doi.org/10.1007/s10509-017-3210-0. Seyfert 1 galaxies are characterized by broader Balmer (Hβ) emission lines (normally on a spectrum based on line strength of Seyfert 1.2, 1.5, 1.8, and 1.9), whereas Seyfert 2 galaxies are characterized by a higher ratio of [OIII] / Hβ ≥ 3 in their spectra. Using a FracDev parameter in R language to classify the morphologies, the authors found that Seyfert 1 galaxies have more active AGNs than Seyfert 2 galaxies, and this is accompanied by a greater deviation or divergence in FracDev morphologies from those of normal galaxies in these figures, greater at lower than an higher redshifts:

Empirical results of the Seyferts vs normal galaxies based on FracDev morphology scores, magnitudes, and averages in FracDev morphology scores vs redshift.

Chen & Hwang (2017) figures.

In brief, there is evidence of a galactic morphology / age-dependent intrinsic (non-Hubble relation) component to galactic redshifts, which doubtless contributes to the 'fingers of god' phenomenon, and it is related to the proximity and apparent age of galaxies to apparent ejection phenomena from AGNs. These data cannot be ignored. We don't and we won't.