The quantized redshift (QR) 'community' has become increasingly insular and isolated - generally referencing only papers of other advocates and avoiding rigorous tests of their methodologies. Hartnett continues this 'tradition' by only referencing older works which have since been superceded. The 'tests' of his methods which he mentions in his papers are also particularly weak. The key issue is that a 1-D power spectrum installs an implicit assumption of spherical symmetry in a dataset, since is it only measuring radial separation. It is no surprise that such a method implies concentric shells centered on our galaxy.

The main astronomical community was initially curious about suggestions of a possible new property of the extragalactic redshift. However, they quickly abandoned interest in the idea when it was demonstrated that noise and clumping in the galaxy distributions could create large peaks in simple 1-D power spectra. These simulated peaks were equivalent to the peaks 'discovered' by the QR advocates (Newman Haynes & Terzian 1989, 1994, Kaiser & Peacock 1991, Newman & Terzian 1995, 1996).

One positive consequence of the quantization claims is that it did spur more research into determining just what information could be extracted from such analyses on the large extragalactic surveys which were being conducted. The ability to determine statistics of large-scale structure in the cosmos is important for comparing observations with large cosmological simulations which were also under development.

Kaiser & Peacock (1991) performed an extensive series of analyses developing simulated datasets which demonstrated how the power spectral peaks in works such as Broadhurst et al (1990) could be generated by clumping of otherwise random galaxy distributions. They also demonstrated how the one-dimensional sampling of a three-dimensional dataset can alias power into other frequencies, further confounding interpretations.

While Hartnett acknowledges the work of Kaiser & Peacock (1991), he claims the conclusion of this work, quoting Kaiser & Peacock, “did not prove that unconventional pictures for large-scale structures were ruled out.” Technically true, but deceptive. Kaiser & Peacock (1991) work really meant that the 1-D approach had insufficient sensitivity to identify real peaks in the distribution.

But this type of problem means is you look for a more powerful test...

Methodologies for analyzing these power spectra in full 3-dimensional form were quickly developed, Baumgart & Fry (1991) and Feldman, Kaiser & Peacock (1994) were some of the earliest in this efforts. One of the more important issues which these tests needed to deal with was the fact that even the most recent sky surveys did not uniformly sample the sky, in terms of direction, and even distance. This issue created 'window functions' which could alias power into other frequencies, creating problems for interpretation (Feldman Kaiser & Peacock 1994). More recently, tutorial-style publications have described more details of the 3-D analysis process (Hamilton, 2005a,b).

The basics of the proper methods have been around over a decade.

Hartnett completely ignores these modern tests. Why does Hartnett limit his work to a one dimensional analysis when he has read the documentation (Kaiser & Peacock 1991) of the flaws in his methodology??

Consider Hartnett's behavior from a more personal analogy: Would you go to a doctor who insisted on conducting tests that could not conclusively identify your ailment? Suppose they insisted on using the inconclusive tests even when better tests were available?

Others have completed these power spectra calculations on the 2dFRS and SDSS 5th data release using modern methods (Cole et al 2005, Percival et al. 2007). Not surprisingly, their results show no evidence of claimed periodicity.

References

- W. I. Newman, M. P. Haynes, and Y. Terzian. “Double galaxy redshifts and the statistics of small numbers”. Astrophysical Journal, 344:111–114, 1989.
- T. J. Broadhurst, R. S. Ellis, D. C. Koo, and A. S. Szalay. “Large-scale distribution of galaxies at the Galactic poles.” Nature, 343:726–728. 1990.
- N. Kaiser and J.A. Peacock. “Power-spectrum analysis of one-dimensional redshift surveys” ApJ 379, 482 (1991)
- D. J. Baumgart and J. N. Fry. “Fourier spectra of three-dimensional data”. Astrophysical Journal, 375:25–34, July 1991.
- W.I. Newman, Martha P. Haynes, and Y. Terzian. “Redshift data and statistical inference”. Astrophysical Journal, 431:147–155, 1994.
- H. A. Feldman, N. Kaiser, and J. A. Peacock. “Power-spectrum analysis of three-dimensional redshift surveys”. Astrophysical Journal, 426:23–37, May 1994.
- W. I. Newman and Y. Terzian. “Power spectrum analysis and redshift data”. Astrophysics & Space Science, 244:127–142, 1996.
- A.J.S. Hamilton. “Power Spectrum Estimation I. Basics” ArXiv Astrophysics e-prints, March 2005.
- A. J. S. Hamilton. “Power Spectrum Estimation II. Linear Maximum Likelihood”. ArXiv Astrophysics e-prints, March 2005.
- S. Cole, W. J. Percival, J. A. Peacock, P. Norberg, C. M. Baugh, C. S. Frenk, I. Baldry, J. Bland-Hawthorn, T. Bridges, R. Cannon, M. Colless, C. Collins, W. Couch, N. J. G. Cross, G. Dalton, V. R. Eke, R. De Propris, S. P. Driver, G. Efstathiou, R. S. Ellis, K. Glazebrook, C. Jackson, A. Jenkins, O. Lahav, I. Lewis, S. Lumsden, S. Maddox, D. Madgwick, B. A. Peterson, W. Sutherland, and K. Taylor. “The 2dF Galaxy Redshift Survey: power-spectrum analysis of the final data set and cosmological implications”. Monthly Notices of the Royal Astronomical Society, 362:505–534, September 2005.
- W. J. Percival, R. C. Nichol, D. J. Eisenstein, J. A. Frieman, M. Fukugita, J. Loveday, A. C. Pope, D. P. Schneider, A. S. Szalay, M. Tegmark, M. S. Vogeley, D. H. Weinberg, I. Zehavi, N. A. Bahcall, J. Brinkmann, A. J. Connolly, and A. Meiksin. “The Shape of the Sloan Digital Sky Survey Data Release 5 Galaxy Power Spectrum”. Astrophysical Journal, 657:645–663, March 2007.

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