Unexpected redshifts

1930: H₀ = 558 km s⁻¹ Mpc⁻¹
Intervening years: H₀ = 30-100 km s⁻¹ Mpc⁻¹ Today, although narrowed, we still have a range of values: H₀ = ~63-75 km s⁻¹ Mpc⁻¹

^{Above, we see
the 2004 estimates of the SN1a acceleration data compared
with various HBBC models with chosen proportions of 'dark
energy' and 'dark matter' (Kirshner, 2004; link).

Their review was in many ways far too simplistic to fully
consider the magnitude and complications of the ad hoc
free-parameter fitting required in HBBC models.}

^{In the NASA
website of the Lambda working group, they attempted to
provide a summary of the many estimated values of the Hubble
constant}^{H₀
from a series of major studies done from 2001 to 2021. This
serves to highlight the difficulties of nailing down this
supposed constant:}

For a few examples, de Jaeger et al. (March 2022) in their attempts to resolve the "Hubble tension" tried the following: using "13 SNe~II with geometric, Cepheid, or tip of the red giant branch (TRGB) host-galaxy distance measurements" derived H₀ = 75.4 +3.8/− 3.7km s⁻¹ Mpc⁻¹ (statistical errors only), which they claimed was " consistent with the local measurement but in disagreement by ~2σ from +ΛCDM value." Also, de Jaeger et al. using Cepheid variables only with a sample size of N = 7, arrived at H₀ = 77.6 + 5.2/− 3.7 km s⁻¹ Mpc⁻¹ , and when using only red giants (TRGB) with a sample size of N = 5, found H₀ = 73.1 + 5.7/− 5.3 km s⁻¹ Mpc⁻¹ . They further claim they did not find that the SNe~1e or the Cepheids were the source of the "H₀ tension" while admitting that their "conclusions rest upon a modest calibrator sample," and urge that larger studies be done in future ( arXiv:2203.08974).
In April 2022, Cao & Ratra (2022) claimed to use non-CMB and "model-independent determinations" with " updated Hubble parameter and baryon acoustic oscillation data, as well as other lower-redshift Type Ia supernova, Mg II reverberation-measured quasar, quasar angular size, H II starburst galaxy, and Amati-correlated gamma-ray burst data, to jointly constrain cosmological parameters in six cosmological models," to arrive at H₀ = 69.7 +/− 1.2 km s⁻¹ Mpc⁻¹ , " the flat ΛCDM model is most favored but mild dark energy dynamics and a little spatial curvature are not ruled out" ( arXiv:2203.10825).
In March 2022, Hu & Wang (link) reported that the "Hubble crisis" may be relieved by having H₀ change over cosmic time from the early universe to the present epoch (arXiv:2203.13037). Anand et al. in March of 2022 instruct the reader to "worry no more, the Hubble tension is relieved" because they made local cosmic measurements using inferences from sedimentary and eclipse-based data of the lunar recession velocity to arrive at H₀ = 63.01 +/− 1.79 km s⁻¹ Mpc⁻¹, which they tout as the first single-step, model-independent measure of the Hubble constant, which also is not far from CMB and the ΛCDM model determinations, concluding that local measurements are the source of the Hubble tension ( arXiv:2203.16551).
In April 2022, Liu et al. also claim a model-independent cosmography method of directly measuring by reconstructing distance based on cosmic chronometer and gravitational lensing observations, as well as a measurement of space-time curvature, while avoiding the polynomial curve-fitting and what the polynomial coefficients might physically mean: H₀ = 72.24 +2.73/− 2.52 km s⁻¹ Mpc⁻¹ (arXiv:2204.07365). When assuming a flat universe in advance, they arrive at H₀ = 70.47 +1.14/− 1.15 km s⁻¹ Mpc⁻¹ , between the Planck CMB and the SH0ES observations.
In late April, the large group of Kenworthy et al. ( arXiv:2204.10866) used a 3 rung distance ladder of calibrating Type Ia supernovae using a SH0ES measurement for the host galaxies of 35 Cepheid variables at cz < 3300 km s⁻¹ , geometrically calibrated in our Milky Way, NGC 4258, and the Large Magellanic Cloud (LMC), and arrived under various assumptions including peculiar velocities at z ~ 0.01 at a range of H₀ = 71.8 to 77.0 km s⁻¹ Mpc⁻¹ . By combining the four best fitting selection models, they estimated H₀ = 73.1 to 77.0 km s⁻¹ Mpc⁻¹ , which is 2σ removed from the Planck results.
Also in April 2022, Garnavich et al. ( arXiv:2204.12060) compared infrared surface brightness fluctuations (IR SBF) in galaxies hosting type Ia supernovae (SNIa) to distances estimated by SNIa light curve fitting, showing that IR SBF estimates are different from those derived from Cepheid variable calibrators. Using IR SBF results from massive galaxies surveye within ~100 Mpc by Jensen et al. (2021; arXiv:2105.08299), Garnavich and colleagues arrived on basis of 25 SNIa host galaxies at H₀ = 74.6 +/− 0.9(stat) +/− 2.7 (syst) km s⁻¹ Mpc⁻¹ , including both statistical errors and systematic errors, and thus consistent with supernovae distances calibrated with Cepheids.
In early May 2022, Renzi and Martinelli ( arXiv:2205.03396) propose that using super massive black hole (SMBH) shadows on galaxies as a distance anchor in the distance ladder, in place of Cepheids for example, will be able to constrain H₀ values within H₀ ≈ 10% for current ground based interferometers and within H₀ ≈ 4% for future interferometers.

Another team in May 2022, Breuval et al (including Adam Riess; arXiv:2205.06280) added an improved calibration for the wavelength dependence of metallicity on the Cepheid Leavitt law, and cepheid brightness does depend on metallicity. Why such a calibration needs to be done of course drops a hint indirectly that other factors need to be taken into account when considering galactic redshift, not limited to be a result of space-time expansion. (More on that).
Reviewing developments, Blanshard et al ( arXiv:2205.05017) in May of 2022 reviewed the tensions in the measurement of H₀ and estimates of matter density within the ΛCDM and some "alternative cosmological models" (CDMs without Λ) highlighting the tensions. They say that data on cosmic chronometers allow derivation of an accurate value at H₀ = 67.4 +/− 1.34 km s⁻¹ Mpc⁻¹ . Nevertheless, they came to the conclusion that the ΛCDM model is "alive and well" but has "an unknown bias in the Cepheids distance calibration" and celebrate a remarkable agreement for the model, statistically better than the previously proposed extensions with H₀ ~ 73.
In late May 2022, Chen et al ( arXiv:2205.11278) arguing that gravitational waves (GW) are another way to probe the Universe's expansion history, and adopt the assumption that binary black hole (BBH) coalescent events involve black holes detected by LIGO-Virgo-KAGRA (LVK) collaboration are primordial in origin, using 43 BBH events from the third LVK GW transient catalog (GWTC-3). Using three PBH mass models and some Bayesian population analysis, they concluded that the constraints on the ΛCDM model cosmological parameters "are rather weak and in agreement with current results." When combining in a measurement from GW170817 (a LIGO / Virgo GW signal of merging neutron stars detected in 2017 in NGC 4993), they were able to claim constraint of H₀ between 69 +19/− 8 km s⁻¹ Mpc⁻¹ and 70 +26/− 8 km s⁻¹ Mpc⁻¹ , comparable with results from phenomonological models of astrophysical mass models of BH coalescence.
In mid May 2022, Schiavonne et al ( arXiv:2205.07033), in examining a collection of 1048 Type Ia Supernovae (SNe Ia) in the Pantheon sample database with a redshift between 0 < z < 2.26, looked to see if the H₀ tension may be found among SNe Ia data using binned statistical analysis with the MCMC method for each bin, considering the ΛCDM and the w₀w_aCDM cosmological models. They observed that H₀ evolves with redshift using a fitted function, H₀(z) = ^~H₀(1 + z)⁻ ^α where ^~H₀ and α are two fitting parameters. Extrapolating with ^~H₀ back to the redshift of the last scattering estimated to be about z = 1100, where they obtain values of consistent with 1σ of the Planck CMB estimates of H₀. So much for heavily model-dependent parameter fitting. However, they do discuss modified gravity models to explain the redshift varying Hubble constant, and make inferences about the postulated involvement of a scalar field potential.

Since JWST. Since becoming fully operational in July of 2022, JWST has not resolved the questions. Just within the arXiv database, a non-quote restricted query for 'measuring the Hubble constant' continues to illustrate the ongoing tensions within and beyond the >CDM paradigm for determining H₀ (1,927 results by 30 May 2024: arXiv query; 1,920 results without 'the': arXiv query). In the more restricted case of the quote-restricted phrase "Hubble tension" query we have 612 results (30 May 2024: arXiv query), whereas for the non-quote-restricted phrase 'Hubble constant' we have 1,386 results (30 May 2024: arXiv query). There is a large burgeoning of attempts to resolve this tension.

Questions: Is the Hubble tension caused by artifacts of instrumentation in different data cohorts? Or is there a paradigmatic reason why such a tension exists? On 28 May 2024, physicist / physics (sometimes cosmology) popular commentator, Sabine Hossenfelder on her YouTube channel suggested that "A huge cosmology problem just might have disappeared" (videolink) citing the November of 2023 paper, which we discuss further by Freedman, W. L. & Madore, B. F. (2023). Progress in direct measurements of the Hubble constant. Journal of Cosmology and Astroparticle Physics (JCAP) 2023, 1-35. JCAP11(2023)050. https://iopscience.iop.org/article/10.1088/1475-7516/2023/11/050/pdf. https://doi.org/10.1088/1475-7516/11/050. Hossenfelder frames the issues succinctly by noting that the Hubble tension is caused by one (any) of the following:

Question for JWST: Has the James Webb Space Telescope (JWST), which became operational in July of 2022, helped this 'tense' situation any? According to a report from November of 2022, Yuan et al. [including 'dark energy' Nobel laureate Adam Riess] (2022. A first look at Cepheids in Type Ia supernova host with JWST. ApJ Letters 940, L17. https://doi.org/10.3847/2041-8213/ac9b27), they found that although not fully optimized for Cepheid observation, with JWST's higher sensitivity in the near-IR part of the spectrum, they were able to mitigate host dust-dimming effects on distance estimates from Cepheid variables in NGC 1365 the host galaxy for distance calibration of SNIa 2012fr for the Hubble constant (H₀). Using a standard star, they did photometry on 31 previously-assayed Cepheids with JWST spanning the period (P) interval from 1.15 < log P < 1.75 including 24 Cepheids with longer P range of 1.35 < log P < 1.75. The period-luminosity (P-L) relations of this cohort was compared to the HST photometry results from 49 Cepheids in the full period range as well as 38 in the longer-period interval. HST and JWST results respectively show good agreement on P-L relations with intercepts (at log P = 1) of magnitudes of 25.74 +/- 0.04 and 25.72 +/- 0.05. The HST-JWST Cepheid photometric consistency shows that there's no HST-'biased-bright' error at the ~0.2 magnitude level which was suggested as a resolution to the 'Hubble tension.' See Yuan et al.'s Figures 1 and 3 below.

Answer: No. The 'Hubble tension' is left unresolved because it is not an artifact of method or instrumentation, but a real feature of the data sets, which again suggests the need for a paradigmatic shift in cosmological theory. The data collected from the world's next generation space observatory, the JWST, is helping in that direction.

Back in 2021, Di Valentino et al. (with an author line including 'dark energy' Nobel Laureate Adam Riess and grand master astronomer Joseph Silk) published a 110 page monograph reviewing >1000 peer-reviewed papers with a title parroting Edwin Hubble's famous 1936 book title, "In the realm of the Hubble tension—a review of solutions" in Class. Quantum Grav. 38, 153001 (https://doi.org/10.1088/1361-6382/ac086d). For their comparison standards, Di Valentino et al. compared this multitude of papers to the Planck 2018 cosmic microwave background power spectrum data with baryonic acoustic oscillations (already loaded with adjustable ΛCDM parameters and yielding an H₀ value centered on 67.36 +/- 0.54 km s⁻¹ Mpc⁻¹, according to Hart & Chluba, 2019) and the combined Pantheon SN1e and latest R20 data from the SH0ES Team Riess et al. (2021, Astrophys. J. 908, L6) with an extrapolation of the Hubble constant, H₀ = 73.2 +/- 1.3 km s⁻¹ Mpc⁻¹ at the 68% confidence level (CL). Like the Planck 2018 data, the SH0ES data set is itself heavily parametrized as indicated in the mere meaning of the acronym itself, "Supernova, H₀, for the Equation of State of Dark Energy" (ESA press release on the 2001-2021 SN data). Excerpted from the many figures of the H₀ values in studies cited in the monograph, one can see the vast degree of parameter-fitting or epicycles-upon-epicycles inserted to try to resolve this supposed constant considered a holy grail of modern cosmology. Even with all of the multitude of attempts to adjust parameters or create epicycles, create complex new models, some appealing to unknown physics, there still is a 4 σ discrepancy between these two standards, or euphemistically we can call it a mere 'tension':

In the excerpted whisker plots from select figures (di Valentino et al. 2021): The vertical pink band equates with the H0 value reported by the Planck 2018 team "within a ΛCDM scenario," while the vertical cyan band equates with the 68% CL estimation of the value based the SH0ES R20 data

Fig. 1 (di Valentinto et al. 2021).

In the spring of 2021, in a blog entitled, "What is the Hubble tension, really? A SH0ES-centric view of the problem," fellow at the Kavli Institute of Cosmology (University of Cambridge), Sunny Vagnozzi posted a humorous "10 commandments for Hubble hunters" satirizing the parameter-fitting required for those seeking to resolve the Hubble "tension." Here is the original version, before he softened and euphemized the "4th commandment" for a visiting lecture:

What's with the Hubble Constant determination Indeterminacy? What is going on with the notorious difficulty of nailing down a consistent, across the galactic constituent population and across cosmic time value of H₀? Is it because H₀? varies over cosmological time? Or is it because too narrow a sample of 'standard candle' bodies and the heavily cosmological model-dependent CMB-based calculations of H₀. What are they missing in the cosmological data?

This following diagram from Risaliti & Luzzo (2019; DOI:10.1038/s41550-018-0657-z) further illustrates the actual diversity of redshift / estimated distance modulus with error bars in the data (including ~1600 quasars marked in yellow just with 1σ uncertainties, or the new [blue-starred marked] quasars with z > 3 from the JLA survey), all illustrating much more redshift-diverse populations of extragalactic objects. When set distance ladder 'standard candle' are not the only objects included, then it becomes obvious that the H₀ relation values are not nearly so tightly constrained as the HBBC model suggests, let alone the highly-parameter-fitted CDM versions.

In actuality, the so-called Hubble 'tension' is far too circumscribed by various parameters of the Big Bang ΛCDM model to even come close to the state of the data regarding the trends in galactic and galactic object redshifts in the Universe. In a lecture a couple weeks later commenting on the early data after the release of the JWST inaugural images in July of 2022, astronomer and plasma cosmologist Eric Lerner with colleague Ricardo Scarpa summarized the the tension between the SH0ES and the model-driven CMB estimates of the H₀ constant, which have now diverged while each being were refined into a ~5σ spread of significance.

Image from Lerner lecture (26 July 2022): "Panic and censorship in cosmology" (link) as well as a link to the 3 papers.

On 22 November 2023, Licia Verde, Nils Schöneberg, & Héctor Gil-Marín released a review paper on the status and meaning of the 'Hubble tension' and attempts to measure and account for it in the quest for a precision cosmology: Verde et al. 2023. A tale of many H₀. https://arxiv.org/abs/2311.13305; https://doi.org/10.48550/arXiv.2311.13305. The authors point out that there are two values around with the measurements cluster: (a) the model-independent determinations from nearby galaxies with standard candles like Cepheid variables and SNIa distance ladder data of H₀ = ~68 km s^-1 Mpc^-1 and (b) the ΛCDM model-dependent determination of H₀ = ~73 km s^-1 Mpc^-1 based on the CMB (for a discussion of the CMB and its interpretation in cosmology, see the yet-to-be-published Chapter IV. The Cosmic Microwave Background (CMB) radiation: From Where and Whence? "As far as the eye can see?"). They suggest that there are three ways to resolve the 'tension' none of which bring consensus to the research community:

The first is to search for systematic errors of interpretation, i.e., the systematics of the distance ladder. If those are missing, then the ΛCDM model needs modification and there are only two ways to 'fix' it:
(i) By altering the physics of the early time (z ≳ 1100) and "thus the early time normalization" of the ΛCDM or
(ii) By making "a global modification" of the model, including questioning the model’s basic assumptions such as the homogeneity of the Universe, the isotropy of the Universe, and the gravitational model of the cosmology.

The authors opine, "The research community has been actively looking for deviations from ΛCDM for two decades; the one we might have found makes us wish we could put the genie back in the bottle."


	TT = temperature power..., TE = temperature-polarization cross..., & EE = polarisation power spectra, respectively.
BAO = baryonic acoustic oscillation.

Verde et al. (2023).

It might be worth suggesting that another option in keeping with all the data would be to look beyond mere 'fixes' of added epicycles to the ΛCDM cosmology. Something is going on which simply does not fit well within our dominant ΛCDM hot Big Bang cosmology (HBBC).

The unorthodox and complicated nature of galactic redshifts. The start of the real problem is that the HBBC paradigm and all it entails has narrowed the focus and research of the teams attempting to determine "the value H₀" by selected from the diversity of object-specific redshifts or z-values in any given cluster or supercluster of galaxies, to see if there is perchance any other causal factors and mechanisms affecting the H₀ redshift relation. So below, we begin to discuss the data which show that in fact there are other causal factors which effect the observed redshifts of various kinds of galaxies and galactic objects which do not conform to the simple Hubble relation. Specific types of galaxies which do not neatly conform to the expected redshifts of the 'standard candles' even if they are apparently in comparable distances. Some of these extragalactic sources include quasars (QSOs), BL Lacertae objects (BL Lac), Seyfert galaxies, blue stellar x-ray objects, ultra-luminous infrared galaxies (ULIRGs), and other types of active galactic nuclei (AGNs) in the clusters and superclusters in which they appear. These associated objects with different redshifts indicate that some component of z may not be cosmic distance related. Some of the first phenomena we would expect to notice then are

(i) unusual scatters in the redshift-distance relationships of large aggregates of galaxies and galactic objects,
(ii) a classification or morpho-type of galaxies with deviating redshift values, and
(iii) associations of objects with differing redshifts in angularly-'close' distance associations.

The evidence for these three phenomena is developed in brief as follows.

^{Unexpected

redshifts in the history of the discovery of the
distance-redshift relationship:}

Log velocity plotted against photographic magnitude (m_pg) indicative of the Hubble relation (Hubble & Humason, 1931; plot taken from Tolman, 1934; from Hoyle et al. 2000).

Galaxy Radial Velocity (z) versus Apparent Magnitude (m). This plot is taken from Lang et al. (1975), they used data from the 'Reference Catalogue of Bright Galaxies' (de Vaucouleurs et al., 1964). There is a high resolution PostScript version of this plot. The above plot was created with Cat's eye (http://tarantella.gsfc.nasa.gov/viewer/example/catseye_intro.html).

Compiled by Allan Sandage, Palomar Observatories: Dashed lines are supposed to represent the effect of peculiar velocities of 1000 - 2000 km/s (cited in Arp, 1998).

Compiled by Halton Arp (1968, cited in 1998), Max Planck Institute: Solid circles = nearby Seyfert galaxies (gen. spiral with very bright, rapidly varying nuclei); 'x's = compact Seyfert-like galaxies; open triangles = QSOs; dashed line represents predicted Hubble relation.

Redshift (v₀) versus distance (Mpc): Ascending Hubble relation according to Arp (1998).

By the early 2000s, the results were showing a scatter where the Cepheid distance ladder calculations showed galaxies nearer than indicated by their redshift (z) values. What was the meaning of these excess redshift values?

We will be returning in several sections to be reposted to the subject of 'anomalous' redshifts.

Although observed by radio frequencies as radio sources since the 1950s, what came to be called quasi-stellar objects (QSOs) or quasars (Chiu, 1964), that is, the radio sources were identified with optical objects in 1962 (Schmidt, 1963; link). These unusual star-like objects with a radio-loud signatures and found to have very unexpectedly high red-shifts, and so according to the Hubble relation were thought to be very remotely distant in the Universe, given the Hubble relation. They are now associated with active galactic nuclei (AGN) in more than one cosmological model.

In the mid-1960s, a series of discussions stirred up by CSSC-associated cosmologists questioned whether the QSOs and their redshifts fit well into the distance-luminosity H₀ models. In a pitched 'battle' between: Hoyle, F. & Burbidge, G. R. 1966. Nature 210, 1846; Hoyle. F. & Burbidge, G. R. 1966. ApJ 144, 634; and Hoyle, F., Burbidge, G. & Sargent, W. 1966. On the nature of the Quasi-stellar Sources. Nature 209, 751. https://doi.org/10.1038/209751a0, and their Big Bang interlocutors, Longair, M. 1966. Evidence on the evolutionary character of the Universe derived from recent red-shift measurements. Nature 211, 949. https://doi.org/10.1038/211949a0; Sciama, D. & Rees, M. 1966. Cosmological significance of the relation between red-shift and flux density for quasars. Nature 211, 1283. https://doi.org/10.1038/2111283a0; Roeder, R. O. & Mitchell, G. F. 1966. Nature 212, 166; and Bolton, J. 1966. Identification of radio galaxies and Quasi-Stellar Objects. Nature 211, 917. https://doi.org/10.1038/211917a0. In their letter to Nature, Hoyle, F. & Burbidge, G. 1966. Relation between the red-shifts of Quasi-stellar Objects and their radio magnitudes. Nature 212, 1334. https://doi.org/10.1038/2121334a0, pointed out that these critics had misrepresented them, and jumped the gun to conclude that the QSO redshifts supported an evolutionary model (short hand for Big Bang cosmology). Sciama & Rees (1966) had gone so far as to say that the QSO redshift data ruled out the steady state (CSSC) cosmologies. Hoyle & Burbidge (1966) pointed out that in fact their interlocutors had jumped the gun, as it were, and that their own goals had been modest, balanced, writing:

"While one can certainly express a personal preference for this latter form of argument. it is overstating the case to claim support from it for one cosmology or another. It appears to us that all these discussions are predicated on the cosmological interpretation of the red-shifts of the quasi-stellar objects, in the sense that this interpretation is taken as axiomatic. Conclusions following from it are accepted, essentially whatever they may be, because a non-cosmological interpretation [non-BB] is taken to be out of the question. In fact, the issue is an open one. The difficulties of the problem, both observational and theoretical, lie in deciding between the cosmological and the 'local' interpretation, not in seeing the implications of either one of them by itself. Throughout our work on this subject, we have been concerned to cover both sides of the problem, rather than to concentrate on one half. By doing so we have been able to place limitations on the kind of model required in the cosmological case, as well as in the local case."

—Hoyle & Burbidge (1966). Nature 212, 1334 [emphasis added].

Near the end of 1975, Lang, K. R. et al. 1975. came up with The composite Hubble diagram. ApJ 202 (3), 583. https://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1975ApJ...202..583, and sought to settle the issue in favor of evolutionary or HBB cosmologies by their analyses of the redshift situation among known QSOs as the situation stood nearly 10 years after the CSSC-HBBC-related arguments above. While they found showed an evolutionary sequence, it was not so much about the rival cosmological models, but about the cosmogony of galaxy evolution, as we shall see. It is important to note that Lang et al. (1975) assumed the old Sandage and colleagues determined H₀ = 50 km^-1 Mpc^-1 and a q₀ = 1.0, when later H₀ had jumped to nearly 70 km^-1 Mpc^-1 or higher (given the 'Hubble tension') and the q₀ had switched sign to q₀ = -1.0, as discussed in chapter III and above.

Lang et al. (1975).

Lang et al. (1975) had indeed found an evolutionary sequence, but with the actual distances of the quasars not yet well-established, it was illusory as support for the HBBC, when it actually suggested something quite revolutionary as far as galactic cosmogony and evolution is concerned.

We turn to summaries of these emerging data showing a QSO scatter of redshifts.

Linear Size versus Luminosity

For 1.4 Ghz radio sources brighter that 2 jansky, the distribution of linear size versus luminosity is a scatter diagram (Condon, 1991).

Redshift versus Spectral Index

The distribution of redshift versus spectral index at 1.4 GHz is also a scatter diagram (Condon, 1991).

Compiled & graphed by L. Greer (1999) from the LBQS data (Hewett et al. 1995).

Compiled & graphed by L. Greer (1999) from the LBQS data (Hewett et al. 1995).

Quasars have been found to have a scatter instead of a good correlation with the Hubble relation:

Redshift (log z) versus apparent magnitude for 7315 QSOs showing a wide scatter
(Hewitt & Burbidge, 1993; cit. in Hoyle et al. 2000).

Locations of the then-known 7315 QSOs projected on Milky Way Galactic coordinates
(Hewitt & Burbidge, 1993; cit. in Hoyle et al. 2000)

Further studies confirmed an intrinsic excess of redshifts in certain AGNs, such as QSOs and even radio galaxies. In pursuit of insights from the Ambartsumian-Arp cosmogony of ejection of higher redshift compact galactic objects from lower redshift AGNs (see chapter IX), Bell, M. B. 2007. (https://arxiv.org/abs/0704.1631) cited, Further evidence that the redshifts of AGN galaxies may contain intrinsic components. ApJ 667 (2), L129. https://doi.org/10.1086/522337, referring to the DIR (declining intrinsic redshifts) post-ejection evolving with increasing luminosity. According to the DIR deductions from the Ambartsumian-Arp cosmogony young AGNs or QSOs evolve into BL Lac objects, Seyfert galaxies, and in the penultimate stage into radio galaxies before losing the rest of their intrinsic redshift and becoming quiescent mature galaxies. Because of low redshift galaxies and high redshift compact sources, we can now infer that the evolutionary pattern Lang et al. espied in 1974 does not show the evolutionary BB cosmology, but the stages of the Ambartsumian-Vorontsov-Vel'yaminov-Arp (AVVA) cosmogony of galaxies (see chapter IX), and a brief introduction below.

The intrinsic redshifts of AGNs suggest that we should expect increased departures from the ordinary H₀ redshift relation with the degree of the energetic activity of AGNs.

Furthermore, quasars began to be found in close apparent connection with nearby, lower redshift galaxies. Low redshift, barred spiral galaxy NGC 1073 with three putatively associated, high redshift QSOs (discovered by H. Arp; cited in Burbidge et al. 1999). Note the alignment of the quasars with the spiral arms. We will return to this and similar associations.

Another local, low redshift galaxy, NGC 3842, with three putatively-associated, more high redshift QSOs in juxtaposition (discovered by H. Arp; cited in Burbidge et al. 1999).

Higher redshift with nearly identical z-values, blue stellar objects in paired-alignment across the minor axis of the Seyfert galaxy NGC 4258 (cited by Arp, 1998 and Burbidge et al. 1999).

In 2002, two more high z objects were discovered in the NGC 7603 system, apparently associated with the same seeming ejection filament (Lopez-Corredoira & Gutierrez, 2002; https://doi.org/10.1051/0004-6361:20020476) indicating a decrease in z with distance from 'parent' galaxy (z = 0.391, 0.243, 0.057).

Later in this website, we'll be exploring the differing redshift associations of 'host' galaxies and apparently associated quasars and other higher z objects. In the meantime, there is an observed pattern as illustrated in the redshift vs. angular separation for 392 galaxy-QSO pairs plotted on a logarithmic scale, indicating an inverse relation between (ascending) angular measure and (descending) redshift, strongly indicative of ejection and at least some connection between higher z values and proximity to ejection. Hatched regions indicate areas excluded by selection effect, i.e., determining whether a galaxy-QSO 'pair' is actually observed (Burbidge et al. 1990; Hoyle et al. 2000).

In another study, about 300 galaxy-QSO pairs were plotted by angular separation (modified from Burbidge et al. 1990; Narlikar 1993). The dotted line indicates what would be expected from a random background distribution of QSOs without any pairing or galaxy-QSO associations.

In yet another study, 197 galaxy-QSO pairs were plotted by angular separation, and again, the non-random pattern of association was assayed (Burbidge et al., 1990; Hoyle et al. 2000).

Another non-Hubble relation redshift phenomenon which we now explore in some detail are the patterns observed starting in the late 1960s that redshifts tend to cluster in a periodic way around certain preferred values of z at least in our cosmic neighborhood. In Burbidge, G. R. & Burbidge, E. M. 1967. Limits to the distance of the Quasi-Stellar Objects deduced from their absorption line spectra. ApJ 148, L107. https://ui.adsabs.harvard.edu/abs/1967ApJ...148L.107B/abstract, a clustering around these values for z was pointed out:

[Image from Burbidge, G. 2003. NGC 6212, 3C 345, and other Quasi-stellar Objects associated with them.
ApJ 586, L119. https://iopscience.iop.org/article/10.1086/374793/fulltext/16874.text.html#crf14].

In 1973, Bell, M. B. & Fort, D. N. A quantitative alternative to the cosmological [Hubble relation] hypothesis for quasars. ApJ, 186, 1. https://articles.adsabs.harvard.edu//full/1973, published a quantitative equation to summarize the data for quantized or periodic redshifts departing from a simple, linear Hubble relation: (1 + z) = (1 + z_c)(l + z_x), where they divided z into a cosmological or Hubble component, z_c, and into a component of unknown origin, z_x.

Brief Excursus on the Ambartsumian-Arp galactic ejection cosmogony hypothesis (for more, see forthcoming Chapter IX). Cf. Arp, 2003. Catalogue of Discordant Redshift Associations; pp. 13-16. The clustering of redshift quantities around certain "preferred values" was discovered by Burbidge & Burbidge (1967. Limits to the distance of the Quasi-Stellar Objects deduced from their absorption line spectra. ApJ 148, L107. https://www.adsabs.harvard.edu/full/1967ApJ). K. G. Karlsson (1971. Possible discretization of quasar redshifts. Astron. Astrophys. 13, 333. https://adsabs.harvard.edu/pdf/1971) showed that these discrete values follow an empirical relationship, (1 + z₂) / (1 + z₁) = 1.23, where z₁ = the lower redshift and z₂ = the next higher redshift up (Arp, 1998. Seeing Red: Redshifts, Cosmology, and Academic Science. Apeiron Press; p. 203) yielding preferred redshift peaks or periodicities in a geometric series or Karlsson series, where z₁ = or corresponds to z_iand z₂ = or corresponds to z_i_{+
1}, with terms reordered thus:

Karlsson showed that the first six elements of the series were observed in the available redshift data, and further he predicted the existence of the next higher peaks with values of z = 2.64 and 3.48. So, given that we repeatedly observe pairs of quasars or other higher redshift compact objects juxtaposed across the minor axis of lower redshift active galaxies as if ejected in pairs from the putative parent galaxy with its lower redshift (z_G), suppose that we consider the putatively ejected pair of quasars with their measured redshifts (z₁, z₂) for example across NGC 4258 (in the figure above), we can relate them to the parent galaxy redshift (z_G) by correcting their redshifts to be in the reference frame or rest frame of the active center of the parent galaxy (z_G), i.e., z_Q, related by (1 + z_Q) = (1 + z₁) / (1 + z_G). The difference between z_Q and the next Karlsson peak in the series is assumed to predict the actual velocity of ejection, v_ej in units of c, that is, (1 + v_ej) = (1 + z_Q) / (1 + z_p), where z_p = the redshift of that nearest Karlsson periodicity peak. For more details see forthcoming Chapter IX.

For now, we note that empirical preferential clustering of redshifts around certain values began to be observed.

Modified from figure 8-4 in H. Arp, 1998. Seeing Red: Redshifts, Cosmology, and Academic Science. Montreal, Quebec, Canada: Apeiron Press.

Power spectrum of the redshifts of 97 spiral galaxies (Guthrie & Napier, 1996; cit. in Hoyle et al. 2000. A Different Approach to Cosmology: From a Static Universe through the Big Bang Towards Reality. Cambridge, UK: Cambridge University Press).

Frequencies of the redshifts of all 7315 then known QSOs with peaks at z ~ 0.3, 1.4, 1.9-2.0. From Hoyle et al. 2000. A Different Approach to Cosmology: From a Static Universe through the Big Bang Towards Reality. Cambridge, UK: Cambridge University Press).

In 2003, a volume was published to honor the late Sir Fred Hoyle (1915-2001) by C. Wickramasinghe, G. Burbidge, & J. Narlikar. (eds.). 2003. Fred Hoyle's Universe. Dordrecht, The Netherlands: Kluwer Academic Publishers, with lots of invited scientists, astronomers, and astrophysicists, on subjects as varied as Hoyle's contributions to people's personal reminiscences, stellar structures and evolution, cosmology, interstellar matter, and panspermia. Among the chapters, two were devoted to redshift periodicities: W. M. Napier on p. 139, republished from A statistical evaluation of anomalous redshifts. Astrophysics and Space Science 285 (2), 419. https://doi.org/10.1023/A:1025452813441.

The hypotheses Napier tested statistically were observations in the light of so-called class of 'anomalous' redshifts for pairs of galaxies and QSOs with widely different z-values, often displaying bridges of luminosity between them. These tests are critical tests of the universality of the Hubble distance relation and whether the HBBC fails the test.

(a) The first claim was that in the galactocentric frame of reference, the Virgo cluster spiral galaxies have a distribution with a periodicity of 71 km s^-1, which is similar to an early claim of 72 km s^-1 in the Coma cluster of galaxies by Tifft, W. C. 1976. Discrete states of redshift and galaxy dynamics. I. Internal motions in single galaxies. ApJ 206, 308. https://ui.adsabs.harvard.edu/abs/1976. Napier (2003) figure 1 shows part of the periodicty / redshift frequency data.

The significance of the 71 km s^-1, periodicity was determined by synthetic simulations of Virgo clusters. The statistical tests were searches of 3-d spaces to find a single I_max, that is, the highest power to be found anywhere in the parameter space of the study. The test results for the real data set of the actual Virgo Cluster are very robust indeed (Napier, 2003; figure 2).

(b) The second claim was that there is a galactocentric periodicity among "wide-profile field [spiral] galaxies" of 36 km s^-1 in the Local Super Cluster (LSC) as reported by Tifft & Cocke. 1984. Properties of the redshift. ApJ 287, 492. https://doi.org/10.1017/S0252921100005546. Napier's more accurate tests showed a 37.5 km s^-1 periodicity in the LSC, as portrayed in Napier, fig. 3.

And in figure 4, which shows a persisting and robust 37.5 km s^-1 periodicity out to 40 cycles, but detectable out to at least 90 cycles, Napier found. This is shown by Arp in 1998 as indicated above, including by a power spectrum test (see figure cited by Hoyle et al. 2000 on the power spectrum of a periodicity of 37.6 km s^-1).

As Tifft and Cocke (1984) had suggested, a robust 37.5 km s^-1 redshift periodicity, in a galactocentric frame of reference, has been found within the Local Super Cluster (LSC). A J statistical test with simulations for artificial LSCs was used to test whether the periodicity is a local or a global effect.

It is indeed a global effect, although more strongly or prominently visible in local groups and associations. The global periodicity of 37.5 km s^-1 was found to be strongly significant statistically, contrary to the predictions of a smooth Hubble relation.

(c) The third claim was that quasars or QSOs clustered around bright local galaxies exhibit a redshift periodicity of 0.89 in log₁₀ (1 + z), although it is not clear whether this is within the galactocentric frame of reference or local periodicities from discrete velocity residuals with respect to the variable solar apex used in assessing the periodicity found in the study of the Virgo Cluster done by Guthrie, B. N. G. & Napier, W. M. 1991. Evidence for redshift periodicity in nearby field galaxies, MNRAS 253 (3), 533. https://doi.org/10.1093/mnras/253.3.533. See also Napier, 1999. Quantized redshifts - New physics or old muddle? Symposium - International Astronomical Union, Volume 194: Activity in Galaxies and Related Phenomena, pp. 290-294. https://doi.org/10.1017/S0074180900162126. What they found was that there is indeed such a periodicity in the distribution of the QSOs appearing around local galaxies.

The work of Karlsson (1990. Astronom. Astrophys. 239, 50) and and that of Burbidge & Napier, 2001; The distribution of redshifts in new samples of quasi-stellar objects. Astrophys. J. 121 (1), 21. https://doi.org/10.1086/318018, was confirmed.

Napier concluded that if all of the above periodicities (a), (b),and (c) are real, then they must be the effects of some single underlying phenomenon and must be connected with the linearity of the local Hubble flow. Again, a cosmology other than the standard HBBC was indicated. We will return to this Burbidge & Napier (2001) paper below, after discussion of Tifft's modeling.

Another paper from the same memorial volume for Fred Hoyle was Tifft, W. 2003. Redshift periodicities, the galaxy-quasar connection. Astrophysics and Space Science 285 (2), 429. https://doi.org/10.1023/A:1025457030279. This paper develops the consequences of a particular decay model for predicting the periodicities in redshift found in various data sets, including the Hubbled Deep Field (HDF) and Hubble Southern Deep Field (SDF), tackling three classes of observations of intrinsic redshifts departing from the linear Hubble redshift relation, (α) characteristic peaks in QSO redshift distributions, (β) associated objects with very discordant redshifts, and (γ) normal galaxy redshift quantization.

Tifft (2003) figure 1 illustrates the periodic quantized redshift distribution for double glaxies (Tifft & Cocke, 1989).

Figure 2 shows the characteristic redshift periods observed globally using concepts which predict the discrete values (Tifft, 1996).

A first principles Planck decay process & the Lehto-Tifft quantization model equations. Although previous work (before 1992) had focused on empirical periodic intervals observed differentially or globally in a galactocentric frame of reference, the emphasis shifted thereafter to the cosmic background frame of reference. Finnish physicist Ari Lehto put forward a mechanism for predicting redshift periodicities (1990. Chinese J. Phys. 28, 15), which Tifft (1996; 1997) tested, confirmed, and developed into the Lehto-Tifft quantization model with a set of equations: Tifft, W. G. 1996. Global redshift periodicities and periodicity structure. ApJ 468, 491. http://dx.doi.org/10.1086/177710; and Tifft, 1997. Global redshift periodicities and variablility. ApJ 485, 465. https://iopscience.iop.org/article/10.1086/304443. In what follows, we closely follow Tifft (2003):

Lehto (1990) planned to describe fundamental particle properties using first principles, namely beginning with the original Planck units of Max himself (link), listed here with their modern values all calculated using 3 fundamental constants in modern values, the velocity of light in vacuo, or c = 2.99792458 x 10⁸ m s^-1 (link), the reduced (divided by 2π, i.e., it's Dirac formulation) Planck constant ħ = 6.582119569 x 10^-16 eV⋅s (link), and the gravitational constant G = 6.674 x 10^-11 m³⋅kg^-1⋅s^-2 (link):

the Planck time (T) = 5.391247(60) x 10^-44 s,
the Planck length (L) = 1.616255(18) x 10^-35 m,
the Planck mass (M) = 2.176434(24) x 10^-8 kg,
and the Planck temperature (Θ) = 1.416784(16) x 10³² K, as well as we should add for reasons later to be apparent,
the coherently derived Planck unit of the Planck energy (L²MT^-2) = 1.2209 x 10¹⁹ eV, converted from joules to electron volts, also for reasons later to be apparent.

Thus, the observed properties of atomic particles, including the redshift, are assumed to emerge from a decay process beginning at the Planck scale in Planck units. Taking this explicit assumption, Lehto hypothesized that the Planck units decay via a period doubling action in factors of 2, commonly observed in chaotic systems. Exploring this, he found apparent ratios involving cube-root powers of 2. Lehto suggested that his hypothetical doubling may happen in a 3-dimensional or 3-parameter space, perceived as 1-dimensional via a cube-root transformation. He predicted that the redshift periods (P) would follow from this doubling under this transformation, such that

(1) P = c2^-^N^/3,

where N is an integer ≥ 0. In applying this to particle physics, we replace c with the Planck mass (M) or energy (L²MT^-2). The above equation is significant in being a general form comparable to Kepler's Third Law in ordinary space, where "a spatial distance relates to the 2/3 power of a time interval,... a unique property of 3-d spaces." This suggests "the possibility that temporal/frequency/energy space is actually 3-dimensional." If such a "3-d temporal space" flows relative to a "3-d spatial space" then the constancy of c and the applicability of special relativity are preserved. "Temporal space" is quantized into a stepwise decay process from the fixed units indicated. In a dynamic 4-space with 3-space and flowing 1-time, there are no such restrictions, so according to Tifft (2003), quantum physics and continuous, infinitesimal classical physics can co-exist.

At this point, Tifft argued that one may re-write equation (1) to distinguish cube-root doubling families thus

(2) P = c2^-^N^/3 = c2^-[(3^D⁺^L^)/3],

where D is the number of doublings and L = 0, 1, 2 to specify which root is utilized. Tifft (2003) points out that equation (2) predicts most redshift periodicities, however to account for all of the observed periodicities, one needs a second cube root to produce 9 9th-root famliies distinguished by a n index T:

(3) P = c2^-^N^/3 = c2^-[(9^D⁺^T^)/9],

Equation (3), claims Tifft (2003), "completely and uniquely describes" all of the periodicities observed as of Tifft (1996, 1997). The index T values are not random, but involve pure doubling, T = L = 0, the dominant relation, followed by a 'Keplerian' T = 6 (L = 2) value, where the odd T values are shifted by 1 as in T = 1, 5, 7 which is less common, and finally the even values of T = 2, 4, 8 are rare or absent entirely. Weirdly, which T family is observed seems to relate to galaxy morphology (Tifft, 1997). Equation (3) seems to describe redshift distributions in local galaxies, whereas at higher redshifts and deeper in space, the T = 0 family "becomes increasingly dominant."

A correction must be made to assess underlying redshift quantization, and that is, redshift intervals "dilate with distance" because of effects both relativistic and geometric, which must be removed. Classically in cosmology, 'curvature' is described by the 'deceleration' parameter q₀, while the Hubble 'constant' serves as a function of time, H = H(t) = f(z, q₀), which in a flat or Euclidean cosmos would have q₀ = 1/2. Removing the z-dependent distortion is called the 'cosmological' correction in redshift. Tifft & Cocke (1984) investigated the 'cosmological' correction for global redshift quantization studies. Tifft (1996) assumed that redshift intervals dilate as √[H(t)] to show a linearization of galaxy redshifts out to >10,000 km s^-1 provided that q₀ = 1/2. Tifft (2003), whose treatment we are following, showed that this correction works well out to z = 1 or 2, far enough to encompass, as we shall see, the Hubble Deep Fields North and South, taken in the 1990s. Following the classical H(t) formulation to find the function H(t) = f(z, q₀), Tifft integrated with a Taylor expansion around q₀ = 1/2 to arrive at a closed relation between z(observed) and z(Lehto-Tifft):

a formulation empirically-fitting all of the then available data (Tifft, 1996, 1997). Tifft (2003) uses equation (4) to convert observed redshift to z(LT) to evaluate redshift quantization. Since equation (4) is consistent with the "temporal 3-d space" model discussed above, where energies vary with temporal volumes as t³ so that if photon redshifts are a result of energy densities, which vary as these volumes evolve, the rate of change will be observed as H = H(t) = f(z, q₀). The spatial volume will evolve as t² so that H = H(t) = f(z, q₀) depends on t² redshift periodicities vary as √[H(t)] exactly as observed.

At this point, let's look at the data which Tifft (2003) summarized in light of the doubling decay process postulated in the Lehto-Tifft model:

Tifft's (2003) Table 1 shows that the redshift peak locations match the empirical logarithmic sequence of QSO redshift peaks observed by Karlsson, K. G. 1977. On the existence of significant peaks in the quasar redshift distribution. A&A 58 (1,2), 237. https://articles.adsabs.harvard.edu//full/1977. Tifft (2003) figure 3 shows the quasars known in 1977.

When one adds the full set of the 3rd Cambridge catalog of quasars, one gets the results in Tifft (2003) figure 4. In addition, one can add the quasars from studies referenced involving the "south galactic cap field" in Tifft (2003) figure 5, differentiated by filled and open circles.

The Karlsson empirical peaks and the Lehto-Tifft model-predicted peaks continue to pile higher (Tifft, 2003, fig. 6) when all of the data from the galactic southern hemisphere south of the initial field are included as found in the QSO and active galaxy catalogue of Veron-Cetty & Veron 1996. 7th ed. A Catalog of Quasars and Active Galaxies. ESO Scientific Report 17. See https://heasarc.gsfc.nasa.gov/W3Browse/all/veroncat.html. Tifft (2003) figure 7 shows that there may be a c/8 peak also.

The trend is extended not on from the c/8 region but also to the c/16 region of the graph when data from Schmidt, M. & Green, R. F. 1983. Quasar evolution derived from the Palomar bright quasar survey and other complete quasar surveys. ApJ 269, 352. https://articles.adsabs.harvard.edu/full/1983ApJ, as illustrated in Tifft (2003) Figure 8.

The Lehto-Tifft model suggests that ongoing Planck unit decay would also yield less active QSOs and ordinary galaxies, thus linking galaxies and quasars. Decay from the first doubling would show a c/2 associated with z = 0.6 quasar peak. The redshift 'spectrum' would be T = 0 dominant, have various decay product periodicities, and importantly, "discordant redshift associations where physically related objects have decayed into different, but related states" as has been discussed by Halton Arp and a few others for years. Although local decay has gone to D = 12-16, but at z = 0.5, the model predicts periodicities in D = 4-9, i.e., c/16 - c/512 (20,000+ to 500 km s^-1) range.

In 1995, the Hubble Space Telescope made a deep and long exposure in a small patch in the celestial northern hemisphere called the Hubble Deep Field (HDF), which provided opportunity to examine redshifts of faint and distant galaxies.

This hypothesis could be tested in 2003 with the Hubble Space Telescope (HST) Hubble Deep Field (HDF) and Southern Deep Field (SDF), in Tifft (2003) Figure 9, as adapted from Cohen et al. 2000. Caltech faint galaxy redshift survey. X. A redshift survey in the region of the Hubble Deep Field north. ApJ 538 (1), 29. https://iopscience.iop.org/article/10.1086/309096/pdf. .
.

Tifft's first study (1997) used the data from Cohen et ai. 1996. Redshift clustering in the Hubble Deep Field. ApJ 471 (1), L5. https://iopscience.iop.org/article/10.1086/310330. That analysis is seen in Tifft (2003) Figure 10. The model predicted T = 1 and T = 6 values are present, especially at the c/2, c/16, and c/32 peaks.

Tifft (2003) Figure 11 showed how precise is the fit to these three peaks, and where the strongest peak was. However, a larger sample was needed and became available with Cohen et al. (2000) as illustrated in Tifft (2003) Figure 12.

Tifft (2003) Figure 13 shows the main peaks as well as some "satellite peaks ... offset slightly" from the predicted c/32 and c/16 peaks. Note that all of the fractions are odd (not even) fractions.

In Tifft (2003) Figure 14, we find the sky positions of the "extended study" region of the HDF within certain z and magnitude (m) values, designations of galaxy clusters (~1 Mpc), and also marking of the discordant redshift pairs of galaxies. Figure 15 shows where Tifft (2003) asked D. Christein Monte Carlo statistical analysis of the probability of pair association by "angular separation" distribution between pairs of sources with discordant redshifts compared with 1000 random sample displacements (in RA and Dec) of objects in one z peak compared with another. Figure 15 also shows the difference between two peaks separated to the extreme by redshift values equivalent to 25,000 km s^-1, showing evidence of clear physical association.

Tifft's (2003) Figures 16 and 17 show the Monte Carlo association analysis for adjacent peaks with discordant redshift differences equivalent to the moderate 12,000-13,000 km s^-¹ range.

Just as they had done HDF extensions into the higher redshift values, Tifft (2003) extended the search for redshift peaks into the lower redshift values in Figure 18.

Just as satellite 'phase' peaks have been observed around certain values in the HDF, Tifft (2003) Figure 19 shows 'phase' peaks around the value c/16 for the data range of 0.2 < z < 0.46. Figure 20 shows 'phase' or satellite peaks around c/16 for z < 0.5.

The last step in analyzing the lower redshift cohort for Tifft (2003) was to locate their positions on the celestial sphere in RA and Dec (Figure 21), in order to assess which 'clumpings' may represent physical associations between sources with discordant redshifts. Again, there are suggested physical associations of galaxies with discordant redshifts.

The HDF findings were tested on the HDFS. It is no surprise that such periodicities were found there as well in the opposite celestial hemisphere. Tifft (2003) Figure 22 shows sources with redshifts from 0.3 < z < 0.6, and sure enough, there are stark periodicities in the predicted T = 0 around c/64 and c/32, as well as some peaking associated with the T = 6 state.

Tifft (2003)'s Figure 23 shows the 'phase' peaking around the c/32 periodicity in the HDFS.

Summary on the Lehto-Tifft model. The Tifft (2003) study was presented at a conference of friends, colleagues, and some old rivals honoring the widely-loved and admired, great astronomer and cosmologist Sir Fred Hoyle and the quest to "better understand the cosmos that Fred so loved." Sir Fred would have much enjoyed the presentation, pouring over the data, and a bracing discussion. While the Lehto-Tifft model shows a striking agreement of numerical results with a model of redshift periodicity built up from the use of a double decay process from the Planck state, it still is a pattern-fitting empirical model, which only hints at the processes underneath. We note the importance of the model of these astounding data which are so unexplained in standard HBB cosmology, and as the literature cited above references, mainstream cosmologists have tended to dismiss or pretend that the redshift periodicities are not real phenomena. In what follows, we will explore a little more data bringing us up to more contemporary times, and some other possible cosmological models to explain these data. (Other reading and resources can be found at link & link).

Return to the Karlsson periodicity. We return to the Burbidge & Napier (2001) paper. Ever since 2001 with more complete sets of quasar data, Burbidge, G. & Napier, W. M. [2001. The distribution of redshifts in new samples of Quasi-stellar Objects. AJ 121 (1), 21. https://doi.org/10.1086/318018] found direct observational evidence for the next set of predicted by the Karlsson formula of redshift periodicity peaks, z = 2.63, 3.45, and 4.47, beyond what had been empirically observed up to then. In careful fashion, Burbidge & Napier (consulting with Margaret Burbidge and Sir Fred Hoyle) not only ran statistical tests but laid out the possible interpretations or hypotheses to explain these data.

With the QSO data available in 2001, the Karlsson periodicity continued to appear and extend beyond and confirming previous predictions.

In 2009, Burbidge & Napier published another paper, Associations of high-redshift Quasi-Stellar Objects with active, low-redshift spiral galaxies. ApJ 706 (1), 657. https://iopscience.iop.org/article/10.1088/0004-637X/706/1/657, where they were able to affirm that the statistically-robust associations between higher redshift quasars and lower redshift galaxies in earlier data sets remained, but were unable to reproduce the results with a partial data set from the SDSS at that point. The observations suggesting associations between low redshift active galaxies and higher redshift continued to build on the trend since the 1950s and 1960s, where the Ambartsumian-Arp ejection cosmogony of galaxies recommends itself as a model (see the discussion in chapter IX. Vast jets and galactic ejection phenomena: Mass origin-ejection?).

Shortly before courageous and persistent dissident observational astronomer Halton Arp's death, more results were published on the 2dF survey in Fulton, C. C. & Arp, H. C. 2012. The 2df Redshift Survey. I. Physical association and periodicity in quasar families. ApJ 754 (2), 134. https://doi.org/10.1088/0004-637X/754/2/134. They examined data from the 2dF Galaxy Redshift Survey (2dFGRS) and from the 2dF Quasar Redshift Survey (2QZ) in the two declination strips at Dec 0^o and -30^o. In order to avoid a range of mixed redshifts of galaxies and quasars, they filtered out all but quasars z ≥ 0.5. Making no mention of the Lehto-Tifft model, Fulton & Arp searched for Karlsson-type periodicity in quasar redshifts. Around each galaxy, they detected quasars which conform to "empirically derived constraints based on an ejection hypothesis." They "ran Monte Carlo control trials against the pure physical associations by replacing the actual redshifts of the candidate companion quasars with quasar redshifts drawn randomly from each respective ... [R.A.] hour." When properly constrained for quasar z grouping and the Karlsson periodicity, the 2dF data showed that the Karlsson periodicity is statistically significant, and not a selection effect (Fulton & Arp, 2012; Figure 5).

Fulton & Arp (2012) Figure 6 shows that the presence of discordant redshift data between physically connected galaxies and quasars has been shown to be statistically significantly.

One of the more recent papers which has attempted to pull together the data on redshift periodicity and compare theoretic explanations was first submitted for publication in 2016, but only published in 2020, indicating the ongoing difficulty of suggesting alternative hypotheses for unusual phenomena in cosmology, and getting them published. That paper is from an Indian group, Mal et al. 2020. Periodicity of quasar and galaxy redshift. Astron & Astroph. 643, A160. https://doi.org/10.1051/0004-6361/201630164. They briefly and informally review >5 decades of published research on periodic redshift data. As already noted, there have been empirical / numerical formulations of the periodicities observed. And there've been attempts, as seen above, to model the causes of the observed periodicities. For example, Depaquit, S., Pecker, J. C. & Vigier, J. P. 1985. Astron. Nachr., 306 (1), 7. https://adsabs.harvard.edu/full/1985AN, argued that the periodicities were caused by (1) a selection effect from data sampling; (2) the non-randomness of quasar distribution in the Universe, and (3) the presence of Dopplerian / non-Dopplerian contributions to redshift. Lehto (1990. Chin. J. Phys. 28, 215) and Tifft (1997; 2003) proposed their developed explanation, discussed above.

In 2007, Bajan & Flin published a review called, Redshift periodicity. Old New Concepts Phys. IV, 159. http://merlin.phys.uni.lodz.pl/concepts/2007_2/2007_2_159.pdf, in which they reviewed studies published since the late 1960s up to their date on the redshift periodicity issue. In their review they included the famous periodicity published by K. G. Karlsson (1971. Possible discretization of quasar redshifts. Astron. Astrophys. 13, 333. https://adsabs.harvard.edu/pdf/1971) who found peaks empirically predicted in a geometric series: z = 0.3, 0.6, 0.96, 1.41, 1.96, and predicted at 2.63 and 3.46 (Bajan & Flin, 2007; Figure 1), as well as the extensive analysis of Hawkins E., Maddox S. J., & Merrifield M. R. 2002. MNRAS 336 (1), L13. No periodicities in 2dF Redshift Survey data. https://doi.org/10.1046/j.1365-8711.2002.05940.x. (Bajan & Flin, 2007; Figure 2), from the SDSS data set.

Reviewing previous studies and utilizing power spectrum analysis (PSA), as well as a number of possible explanations standard and exotic, Bajan & Flin (2007) concluded that redshift periodicity "among galaxies is not well established" despite there being some effect at the 2σ significance level. See also the review by Bajan, K., Flin, P., Godlowski, W. et al. 2007. On the investigations of galaxy redshift periodicity. Phys. Part. Nuclei Lett. 4, 5. https://doi.org/10.1134/S1547477107010025.

Many years earlier, following in the empirical astronomy trail-blazed path of Viktor Ambartsumian (1954, 1958, 1961, cf. Arp, 1999. Ambartsumian's greatest insight - the origin of galaxies, in Terzian, Y., Weedman, D., Khachikian, E., [eds.], Active Galactic Nuclei and Related Phenomena, IAU Symposium 194, 473; where Arp recounts Jan Oort's privately whispered confession to him in 1973 that 'You know, Ambartsumian was right about absolutely everything'), Narlikar, J. V. & Das, P. K. 1980. Anomalous redshifts of quasi-stellar objects. ApJ 240, 401. https://articles.adsabs.harvard.edu/full/1980ApJ; and Narlikar, J. V. & Arp, H. 1993. ApJ 405 (1), 51. https://adsabs.harvard.edu/full/1993ApJ argue that QSO redshift periodicities are the result of active galactic nuclei (AGN) ejecting quasars, in accord with the even earlier proposal of a scale-invariant Machian 'variable mass hypothesis' of Hoyle, F. S. & Narlikar, J. V. 1964. A new theory of gravitation. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 282, 191. http://dx.doi.org/10.1098/rspa.1964.0227; and 1966. A conformal theory of gravitation. Proc. Royal Soc. London 294 (1437), 138. http://dx.doi.org/10.1098/rspa.1966.0199) developed in the elaborations of the CSSC (classic steady state cosmologies, post-1948; in their C-field formulation).

[Note: In 1965, Stephen Hawking, On the Hoyle-Narlikar theory of gravitation. Proc. Royal Soc. A 286, 313. https://doi.org/10.1098/rspa.1965.0146, argued that the Machian HN theory in its time-symmetric retarded and advanced (going backwards in time) relativistic wave equations in integration would diverge to infinity because of the infinite future. In 2015, Fearn pointed out that because of the Cosmic Event Horizon (CEH, i.e., observer's horizon) in an expanding, accelerating universe, the advanced solutions would not diverge to infinity given the CEH boundary, and hence, Hawking's objection is mistaken. That an ongoing, robust theoretic development can take place, along the HN theoretic approach, is evident in Yadav et al. 2016. C-field cosmological models: revisited. Research in Astronomy and Astrophysics 16 (12), 188. https://iopscience.iop.org/article/10.1088/1674-4527/16/12/188, and in Narlikar (2021), Three pathbreaking papers of 1966 revisited: their relevance to certain aspects of cosmological creation today. EPJ H 46, 21. https://doi.org/10.1140/epjh/s13129-021-00025-6. We will return to this topic].

In light of this rich historical and theoretic background, Mal et al. (2020) in Periodicity of quasar and galaxy redshift. A&A 643, A160. https://doi.org/10.1051/0004-6361/201630164, aimed to test for redshift periodicities using singular value decomposition (SVD) on the Sloan Digital Sky Survey (SDSS) 2dF data which includes >10,000 quasars and >100,000 galaxies from the DR10 and DR12 subsets as well as simulated data. Instead of the usual Fourier transforms, to detect fundamental periods of z in redshift distributions, they applied singular value decomposition (SVD) and unlike Hawkins et al. (2002), they found a multiplicity of redshift periodicities in the SDSS data.

Histograms of the periodicities they detected in the SDSS quasar and galaxy redshift data versus the periodicities detected in the mock data, Mal et al. (2020)'s Figures 7 & 8, and Table 3, respectively.

SVR spectra of redshift periodicities for QSOs and galaxies in the SDSS data in Mal et al. (2020) Figures 9 and 10.

Although it took 4 years to get their paper published, Mal et al. (2020), having reviewed the field of redshift periodicities, made some conclusions on how various theoretical models help explain these phenomena. In the standard HBBC theory, where we have an expanding cosmos which is generally isotropic and homogenous, they point out, the distribution of extragalactic redshifts should be approximately aperiodic and continuous. However, as the data show, they are neither. Since redshift periodicity is really there, Mal et al. in their discussion and conclusions turn to three main theoretical solutions to explain these results:

Mal et al. (2020) suggest that the details of a promising Machian HN theoretic approach remain to be worked out.

In later chapters, we'll also discuss how these phenomena and theoretical considerations are beyond the current New Ptolemaic System paradigm of the ΛCDM Concordance cosmology of the HBBC. We also await the development of the emerging CGC model, by friend and colleague Joe Bakhos, who is taking cognisance of this fascinating and deeply significant class of observations of our Universe. See Bakhos, J. 2022. Chasing Oumuamua: An apology for a cyclic gravity and cosmology, consistent with an adaptation of general relativity. https://vixra.org/pdf/2203.0032v4.pdf, and the further postings at The Taurus Report: https://taurusreport.com/ and its Youtube channel).

"[Because it is outside current theory] most astrophysicists and cosmologists have felt justified in ignoring the evidence for anomalous redshifts, the thought being that what is known to be impossible remains impossible no matter how strong the evidence for it may be. . . [Our] main purpose . . . [in] the present paper is to question this mode of thinking" (Hoyle & Burbidge, 1995).

We will next turn to the phantasmagorical world of radio astronomy and the part it has played in the history of finding a modern scientific cosmology.


	Table 3 continuing with 3C radio sources: z-values in the 4th column: