Here I make a summary of the case for periodicity by listing a selection of papers. This is by no means a comprehensive list nor in any sense a representative one, but it simply includes some papers that I have looked at that argue both for and against periodicity in redshifts. I discuss the methods used, the degree of checking with other samples and why there are differences of opinion about periodicity.

According to reference 16 "Correlation function is the most widely used in studies of large scale structure" and I see no reason to dispute this. It does seem that some large scale periods are found with this method, but at smaller scales the method will wash out the Tifft type periods when done in 3D. This claim will be fully addressed in a following post. I simply note that surveys that simply analyze redshift for periods generally find significant results. However when these other methods are used, particularly at smaller scales then periodicity may not be found. The conclusion is that the periods are there but that the assumption that redshift can be mixed with other dimensions to test for small scale periodicity is invalid as demonstrated by Tifft's results that have been consistently verified,

A. Small scale galaxy periodicity

This includes the 72 km/s quantization and related periods. Almost all of the periods found have been simple ratios to 72 km/s. Most of these have appeared multiple times in papers by different authors. The periods that I contend are real include 144, 72, 36, 24, 18, 12 km/s and perhaps additional smaller ones, but I will just concentrate on this list. It is clear from the papers (and is also expected by HT) that dwarf galaxies have smaller periods than larger galaxies. The periods relate to galaxy pairs, galaxy groups, and whole sky consistency in either the milky way centre frame or the CMBR frame or similar frames to these determined by Tifft. Others have checked for these frames and confirmed them. I have not found any paper that used Tifft's method and reported none of these periodicities.

1. APJ 221:756-775 1978 May 1, The absolute solar motion and the discrete redshift, W G Tifft.
Dwarf galaxies, after removing the solar motion, show 72 km/s periodicity and various multiples of 12 km/s including 36 km/s and 24 km/s. The determined values are 72.135 km/s and 12.0225 km/s. R Tomes notes HT predicts 72.153 and 12.0255 km/s. Many later papers get 72.45 km/s and fractions thereof.

2. APJ 268:56-59 1983 May 1, Redshift Quantization in compact groups of galaxies, W J Cocke and W G Tifft
Compact galaxy groups show a significant 72 km/s periodicity. With less significance 144, 90 and 36 km/s periods also found.

3. APJ 291:88-111 1985 Apr 1, Analysis of groups of galaxies with accurate redshifts, Halton Arp and Jack W Sulentic
Following Tifft's findings of differences withing groups tending to be multiples of 72 km/s, this paper examines that issue. It finds that the differences do indeed tend to be low multiples of 72 km/s. It also finds that the main galaxy in a group tends to have a lower redshift than its companions. This is an argument for internal redshifts. Arp made an error in his statistics, but the result is still true. R Tomes notes this is somewhat similar to the O and B type stars having an offset in redshift relative to other stars.

4. APJ 345:72-83 1989 Oct 1, Periodicities in Galaxy Redshifts, Martin R Croasdale
Using new data Croasdale tests for Tiffts periods of 72, 36 and 24 km/s. He uses Monte Carlo simulations to check on the statistical probabilities, so the paper is very solid statistically. He also checks for the difference between periods in z and in ln(1+z) and finds that the periods are present only in z. The sample is deeper than Tifft's and so this conclusion should over-ride Tifft's. He uses a whole sky frame and Tifft's bases of reduction to that frame based on our motion. The estimates of the errors in the measured values are 72.45+/-0.3, and 24.15+/-0.1 km/s. R Tomes notes that these error margins place Tifft's values at 1 s.d. from HT predictions. R Tomes further notes that the periodicty in z and not ln(1+z) also shows up in some other places and leads to the conclusion that this idea of Arp, Tifft and Tomes should be revised. It would appear that some aspect of development of the universe is over-riding this natural assumption.

5. 1991MNRAS 253 533-544, Evidence for Redshift Periodicity in nearby filed galaxies, B N G Guthrie amd W M Napier
Set out to check Tifft's findings. Find 37.2 km/s periodicity at p~10^-5 level. Whole sky periodicity with results in the galaxy frame.

6. APJ 385:32-48 1992 Jan 20, Velocity Differences in Binaary Galaxies I...., Stephen E Schneider and Edwin E Salpeter
Performing a check on Tifft's binary galaxies using new data, they found multiples of 72 km/s at low multiples only 0, 72, 144 km/s), then a smooth curve with no peaks at 216 km/s and beyond.

7. J Astrophys Astr 1997 18:415-433, Redshift quantization in the CMBR frame, W G Tifft
Tifft finds that by using the CMBR frame the periodicities are visible over the whole sky. In addition to the 72 km/s period he finds 36.6 km/s, 18.3 km/s, 10.67 km/s, 9.15 km/s, and some shorter periods.

8. J.Astrophys.Astr. 1997 18:455-463, Quantized Redshifts: A Status Report, W M Napier & B N G Guthrie
71.5 km/s in Virgo Cluster p<10^-4 and 37.5 km/s global p<10^-3 to galaxy frame, V=213 km/s 93 d, 2 d.

B. Large scale galaxy periodicity

The most commonly reported and discussed periodicity is 12,800 km/s (often referred to as 128/h Mpc or z=.043). Other related periods are found such as 4,300 km/s which is 1/3 of that figure. I have often found 4,300 and 8,600 km/s periodicities in galaxy samples, but this is unpublished analysis. The 12,800 km/s period in particular has been shown to produce a near cubic lattice of galaxy superclusters.

9. ARAA 1991 29:499-541, Redshift Survey of Galaxies, Riccardo Giovanelli and Martha P Haynes
Shows in Figure 1 the histogram distribution of a large number of galaxies in 500 km/s bins up to 30,000 km/s. My analysis of the histogram shows a clear 4,300 km/s periodicity.


10. arXiv:astro-ph/9710207v1 1997 Oct 20, Regularity in the distribution of superclusters, Martin Kerscher
"Using a measure of clustering derived from the nearest neighbour distribution and the void probability function we are able to distinguish between regular and clustered structures. With an example we show that regularity is a property of a point set, which may be invisible in the two point correlation function. Applying this measure to a supercluster catalogue we conclude that there is some evidence for regular structures on large scales."

11. 1992A&A 257 1M, Typical scales in the distribution of galaxies and clusters from the unnormalized pair counts., H J Mo, Z G Deng, X Y Xia, P Schiller, G Borner
Conclusions: At around 130, 60, 25, 16 Mpc/h significant periodicities found. They use a method that avoids some problems with previous methods in finding periods.

12. Nature 385, 112 - 113 (09 January 1997), The Universe as a lattice, Robert Kirshner
I cannot access this paper. The title is interesting. Perhaps this is related to the following one.

13. arXiv:astro-ph/9701018 1997 Jan 6, A 120 Mpc periodicity in the three dimensional distribution of galaxy superclusters, J. Einasto, M. Einasto, S. Gottl¨ober, V. M¨uller, V. Saar, A. A. Starobinsky, E. Tago, D. Tucker, H. Andernach, P. Frisch
Shows 3D lattice of 120 Mpc (+/-20) in galaxies in a near cubic lattice.


14. THE ASTROPHYSICAL JOURNAL, 519:441È455, 1999 July 10, STEPS TOWARD THE POWER SPECTRUM OF MATTER. I. THE MEAN SPECTRUM OF GALAXIES, J. EINASTO, M. EINASTO,E. TAGO, A. A. STAROBINSKY, F. ATRIO-BARANDELA, V. MU. LLER, A. KNEBE, P. FRISCH, R. CEN, H. ANDERNACH, AND D. TUCKER
"We calculate the mean power spectrum of all galaxies using published power spectra of galaxies and clusters of galaxies." ... "Their mean power spectrum has a spike at wavenumber k=0.05+/-0.01 h Mpc^-1, followed by an approximate power-law spectrum of index n~=1.9 toward small scales." R Tomes notes that the k=.05 translates to a ~126 Mpc/h period, and that the whole spectrum changes at this peak. In other words above that scale the power law changes dramatically.

C. Quasar, absorption systems etc

There have been reports of a z=.06 quasar peak and periodicity as well as a periodicity in delta ln(1+z)~1.23 and while there are multiple reports on this there are claims based on later samples that the periodicity is not present. This period is therefore uncertain.

15. APJ 359:L33-36, 1990 August 20, The Redshift peak at z=0.06, G Burbidge and A Hewitt.
Refers to past studies finding quasars at regular intervals of delta ln(1+z)=0.206 which I note is equivalent to ratios 1.229 in 1+z. The first peak is at z=0.06 and so the series goes: z=0.06, 0.30, 0.60, 0.96, 1.41, 1.96, 2.63, 3.45. The authors explain that emission line groupings have been shown to not explain the groupings. The average for all the 89 objects in the peak is z=0.0597 and the probability of so many values in one bin is 10^-11. They state that the possible components in a redshift are:
1+z = (1+zc)*(1+zr)*(1+zi) where xc=cosmological redshift, zr=random motion redshift and zi=internal redshift. This is a useful notation because in big bang zi=0 is assumed. The authors note that the Broadhurst find is equivalent to delta z=0.044.

16. APJ SS 75:273-295, A new survey for quasar clustering, Patrick S Osmer and Paul C Hewitt,
Correlation function is the most widely used in studies of large scale structure. They use this and state that no significant periods are found in the sample. However R Tomes notes that in fig 8B repeated peaks clearly occur at 175 Mpc intervals (they do not have a /h and do not specify a Hubble constant, so this is unclear in its meaning).


17. J.Astrophys.Astr. 1997 18, 441-447, Periodicity in the Redshift Distribution of Quasi Stellar Objects, Debiprosad Duari
Finds significant periodicity at delta z=.0565 and delta z=.0128 (less certain). Compares to HT .0577 and (?).

18. THE ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 122:355-414, 1999 June, CLUSTERING PROPERTIES OF LOW-REDSHIFT QSO ABSORPTION SYSTEMS TOWARD THE GALACTIC POLES, DANIEL E. VANDEN BERK, JAMES T. LAUROESCH, CHRIS STOUGHTON, ALEXANDER S. SZALAY, DAVID C. KOO, ARLIN P. S. CROTTS, J. CHRIS BLADES, ADRIAN L. MELOTT, BRIAN J. BOYLE, THOMAS J. BROADHURST, AND DONALD G. YORK
The absorption systems do not show the 128 Mpc/h periodicity found in galaxies, but do show a peak in multiple different samples as 41.5 Mc/h. R Tomes notes that this period is 1/3 of the other and predicted by HT as 43.


19. MNRAS 2007 Mar 12 = arXiv/astro-ph0703277, The redshift distribution of absorption-line systems in QSO spectra, A. I. Ryabinkov, A. D. Kaminker ?, and D. A. Varshalovich
Shows regular absorption line systems at delta z=0.20 intervals for 18 intervals from z=0 to z=3.6, n=2003 with significance at sigma=4.5 s.d. They also discuss time intervals in the vicinity of 600 MY as relevant.

20. 2002IAUS 199 56M, The Luminosity Periodicity of Galaxies and Quasars in the Decametric Range, A P Miroshnichenko http://adsabs.harvard.edu/abs/2002IAUS..199...56M
Significant periodicity in z was found at 2.222, 1.124, 0.448, 0.224, 0.200, 0.192, 0.048, 0.0125. He notes that .048 is close to .043 of Broadhurst and .0125 is close to Duari, Gupta, Narlikar finding. R Tomes notes that these periods show many near or exact harmonic ratios.

21. A&A 242:1-12 1991, Against the delta ln(1+z) ~=.205 periodicity in quasar redshifts, D Scott
He examines the Arp, Burbidge etc argument that quasars show peaks at 1+z=1.06*1.227^n and finds no support for this with a larger database. Although he claims that the prior quasar claimed periods have no consistency, there is actually some.