Where are we in the universe?
by Dr John Hartnett
Fourier analysis of galaxy number counts N(z) calculated for both the large galaxy
surveys, SDSS and 2dF GRS, indicates that galaxies have preferred periodic redshifts.
There are two ways to interpret this data: 1) that the effect is purely in redshift
space and therefore results of some observer bias and/or the universe underwent
past oscillations in its expansion rate, or 2) that it is a real space effect and
due to the physical location of millions of galaxies on concentric shells with regular
spacings. These explanations can be tested and preliminary analysis favours the
latter. If this turns out to be true, it means our galaxy is located about 125 million
light-years from the centre of the largest super-structure of galaxies ever observed.
Figure 1. Sloan Digital Sky Survey (SDSS) map, each point showing
the position of galaxies with respect to Earth at the apex. Their distances were
determined from their spectra to create a 2 billion light-year-deep 3D map where
each galaxy is shown as a single point. This is one half of the published map; the
whole map shows 66,976 galaxies that lie near the plane of Earth’s equator
from the 205,443 galaxies mapped. (From Astrophysical Research Consortium (ARC)
and the Sloan Digital Sky Survey (SDSS) Collaboration,
ref. 1.)
Millions of sources in the cosmos have been located by robotic telescopes and various
data recorded for them. From that, maps have been created that show how the galaxies
are distributed in the sky around our galaxy. Figure 1 shows one such map generated
with many tens of thousands of galaxies. At the apex we find our galaxy, but the
scale of this map is huge. This is from one such survey, the Sloan Digital Sky Survey
(SDSS), and another is the 2 degree Field Galaxy Redshift Survey (2dF#1GRS).
This interpretation also suggests that, at a minimum, the local universe we see
around us has a special place, a centre, and we are there, or nearby.
In a recent paper,2 a colleague
and I showed from the Fourier analyses on galaxy number counts N(z) calculated
for both SDSS and 2dF GRS, that galaxies have preferred periodic redshifts. Discrete
Fourier Transforms were calculated from N(z), the histograms determined
by binning (counting) the observed redshifts of the survey galaxies between z –
δz/2 and z + δz/2 as a function of redshift z, where generally δz
= 10-3 was used. Data for 427,513 galaxies from the SDSS Fifth Data Release
were obtained where the data are primarily sampled from within about -10 to 70 degrees
Right Ascension (RA) from the celestial equator. Also, data for 221,414 galaxies
were obtained from the 2dF GRS where the data are confined to within 2 degrees RA
balanced between the Northern and Southern hemispheres.
The analysis found significant redshift spacings of Δz = 0.0102, 0.0246, and
0.0448 in the SDSS, with significance at a level of at least 4σ,3 and strong agreement with the same analysis from
2dF GRS. If one then applies the Hubble law,4
that is, assumes that the Hubble law,
applies to these relatively low redshift galaxies (z < 0.35) without
assuming any cosmology, then the conclusion one gets is that the galaxies preferentially
tend to be located on concentric shells with periodic real space intervals. These
were determined from Eq. (1) by replacing z with Δz, resulting in
regular real space radial distance intervals Δr. And by combining the results
from both surveys we get Δr = 31.7 ±1.8 h-1 Mpc, 73.4 ±
5.8 h-1 Mpc and 127 ± 21 h-1 Mpc, where the Hubble
constant H0 = 100 kms−1 Mpc−1 and the
parameter h = H0 /100, as used in standard cosmology.
In the usual analysis, in standard cosmology, the spatial two-point or autocorrelation
function is used to define the excess probability, compared to that expected for
a random distribution, of finding a pair of galaxies at a given separation. This
involves the assumption of the Cosmological Principle.5 As a result the power spectrum P(k)
is derived from the two-point correlation function.6 The power spectrum is predicted by theories for
the formation of large scale structure in the universe and compared with that measured,
or, more precisely, calculated from the available data.
The power spectrum P(k) is used to look for mass density fluctuations
on various scales over cosmological time. There it is assumed that looking back
in redshift space is looking back over cosmological time and, in the light of the
Cosmological principle, any density fluctuations are simply evidence of the scale
of clustering at some past epoch (z), since there is no special or preferred frame
to view the universe from.
In deriving P(k), a windowing function (usually a Gaussian) is
applied to reduce the noise seen in the density fluctuations as a function of k
or 1/Δz. But it also has the effect of smoothing out the ‘signal’
we are looking for contained in the ‘peaks’ at small redshift intervals
(1/Δz). After applying this method, without the Gaussian windowing function,
we did still find significant redshift space (actually k-space) periodicity
in both data sets at redshifts intervals consistent with the first two listed above,
ie. at Δz = 0.0102 and 0.0246. However a Discrete Fourier Transform (FT) of
the unsmoothed N(z) data is much more sensitive to finding redshift space
periodicity at smaller values of Δz. And the third significant redshift periodicity,
where Δr =127 ± 21 h-1 Mpc, seen with the FT method, is
the same result discovered by Broadhurst et al. (1990)7 from a pencil-beam survey of field galaxies. The
latter is generally interpreted as the scale of galaxy clustering in the universe.
Also, we applied straight pair counting. Another way to determine if galaxies are
separated by a periodic redshift interval is to build histograms by binning the
number of pairs (Npairs) of galaxies that have the same separation (Δz)
in redshift space, then looking for over abundance peaks in the Npairs
histograms. Since redshifts are measured radially from the observer at the centre
of the distribution this method detects redshift space separation with respect to
that symmetry. As it turned out, it was not so sensitive but did still detect the
first two listed above, i.e. at Δz = 0.0102 and 0.0246.
Finally we did a correlation analysis between the two surveys. We compared N(z)
from each by artificially shifting the redshift of the ith bin (determined
between zi – δz/2 and zi + δz/2) in one survey
and recalculating the correlation function R2 each step. See ref. 2 for
details. There is a significant spatial region of the 2dF GRS that has overlap with
the SDSS and so we would expect R2 for the unshifted bins to show significant
correlation. What we found was interesting. We found a periodicity in the R2
correlation function with a period Δz ≈ 0.027. This is again the main
visible-to-the-eye redshift periodicity in figure 1. Now these results can be interpreted
as either evidence for a real space structure with our galaxy cosmologically near
its centre, or as a redshift space effect where the universe has undergone oscillations
in its expansion rate over past epochs. The latter is what Hirano et al.
(2008)8 advocated and we
referred to in ref. 2.
Either the effect is totally due to the expansion of the universe, and therefore
only a redshift space effect, because redshift is one dimensional, or it results
from real space structure. Since we are only able to sample the radial component
of the redshift, assuming it results from the galaxies moving away from us, then
it would only appear that the galaxies are arranged in rings (or shells
in 3D space) due to the fact that in the past the universe’s rate of expansion
oscillated. If this were the case then it should look like all galaxies are racing
away from the centre and that these rings are centred exactly on the observer, never
off-centre from the observer, not even by a small amount.9
The subtlety here is that one is implicitly assuming that the distribution of galaxies
in the universe must be essentially random on the very large scale with only the
cosmic web of filaments and voids, an assumption from the Cosmological Principle.
Hence anything else you see must be due to some effect other than real space structure.
“What really interests me is whether God had any choice in the creation of
the world”—Albert Einstein10
Figure 2. Albert Einstein during a lecture in Vienna in 1921 (age
42).
However if the effect is a real space effect, it means that the galaxies are physically
situated in concentric shells, which, in an expanding universe, are moving away
from us at the centre. This interpretation also suggests that, at a minimum, the
local universe we see around us has a special place, a centre, and we are there,
or nearby. This idea is at odds with the Cosmological Principle, which remember
has its origin in the notion that there is no Creator, no design and no purpose
in the universe. Therefore, the idea that we may be living at or near the centre
of the universe is abhorrent to all those who hold to atheistic and/or non-biblical
worldviews.
It is not so easy to determine the real space structure of the universe because
we have no independent measure of distance in the universe. So when astronomers
look at a map, like in figure 1, they really are looking at a map of redshifts and
directions in the sky from where the light has come. Then to get the distance to
the source galaxy they have to assume the Hubble law.
But there may be a way to distinguish between the two possibilities. As I mentioned,
if the centre of the large scale structure of galaxies around us coincides with
our galaxy it would suggest that it is purely a redshift effect and not indicative
of real space, though even that would still be impossible to prove because we have
no independent measure of distance. But if the centre of concentric shells of galaxies
coincides at some other point in space then that indicates a real space structure
and not solely a redshift space effect.
In a second paper11 I
found a real space superstructure, possibly involving millions of galaxies, was
favoured, with galaxies preferring to lie on periodically spaced concentric shells
centred on a location about 26.86 h-1 Mpc from here. Certainly, to date,
this has not been ruled out. However, I made the assumption that for small redshifts
it was valid to assume we are looking at spatial distribution of the galaxies in
their redshifts. Then I implemented an algorithm to artificially shift the centre
in real space, recalculate what all the redshifts would be if observed from that
new central point, determine N(z) and recalculate the FT from the new N(z).
I then compared the magnitude of the second Fourier peak (redshift space interval)
to determine where the true physical centre should be. This is where the Fourier
peak amplitude is maximized.
I found that the centre of the concentric shells with Δz ≈ 0.027, which
are most prominently seen in figure 1, does not coincide with our galaxy’s
position in space but that the centre is about 26.86 h-1 Mpc or about
125 million light-years (assuming h = 0.72) from here. That is still a relatively
small distance on the scale of the very large scale of the structure analysed—billions
of light-years in extent.
Near centre of massive super-structure of millions of galaxies
We are here not by random chance but because God created the earth to be inhabited
and He wanted to show us His glory.
The evidence is in favour of this effect being due to real space structure because
the spherical shells of periodic redshift are not centered on our galaxy. If it
was a systematic effect due to observer bias we would expect that the centre of
the shells would coincide with the observer. Though this is still not conclusive,
and more analysis is needed, we have evidence for a supermassive real space structure,
possibly involving millions of galaxies, with our Milky Way located somewhere near
but not actually at its centre.
We are in a special place after all, both spiritually at the centre of God’s
attention and also maybe physically somewhere near the centre of the largest galactic
structure ever observed in the universe. We are here not by random chance but because
God created the earth to be inhabited and He wanted to show us His glory.
“For the invisible things of him from the creation of
the world are clearly seen, being understood by the things that are made, even his
eternal power and Godhead; so that they are without excuse” (Romans 1:20).
And they are without excuse.
Related articles
Further reading
References
- For a more detailed and complete map, where luminosity is
represented by colour, see: www.sdss.org/news/releases/galaxy_zoom.jpg.
Return to text.
- Hartnett, J.G. and Hirano, K., Galaxy redshift abundance periodicity
from Fourier analysis of number counts N(z) using SDSS and 2dF GRS galaxy surveys,
Astrophysics and Space Science 318(1, 2):13–24,
2008; preprint available at: arxiv.org/abs/0711.4885. Return to text.
- I.e. Four standard deviations. Return to
text.
- Hubble law: v = H0 r, where v is the velocity of
the expansion of the universe, as determined by the redshift of the galaxies in
it. Here redshift z = v/c for small redshifts, where c is the speed of light in
vacuum. The distance to the galaxy is represented by r and H0 is the
Hubble constant, which has been very difficult to determine but nowadays lies somewhere
between 55 and 80 km/s/Mpc. Return to text.
- It essentially assumes that the galaxies in the universe are
uniformly yet randomly distributed throughout the cosmos on some very large scale.
Therefore all observers at all locations in the universe at the same epoch should
see the same distribution of galaxies. There are no favoured places. Richard Feynman
succinctly describes the problem of the Cosmological Principle:
“ … I suspect that the assumption of uniformity of the universe reflects
a prejudice born of a sequence of overthrows of geocentric ideas … It would
be embarrassing to find, after stating that we live in an ordinary planet about
an ordinary star in an ordinary galaxy, that our place in the universe is extraordinary
… To avoid embarrassment we cling to the hypothesis of uniformity.”
Feynman, R.P., Morinigo, F.B. and Wagner, W.G., Feynman lectures on gravitation,
Penguin Books, London, p. 166, 1999. Return to text.
- The power spectrum is essentially the square of the Fourier
frequencies in k-space but calculated with a windowing function. Here k=1/Δz
is the inverse of the redshift interval. Return to text.
- Broadhurst, T.J., Ellis, R.S., Koo, D.C. and Szalay, A.S.,
Large-scale distribution of galaxies at the Galactic poles, Nature
343:726, 1990. Return to text.
- Hirano, K., Kawabata, K. and Komiya, Z., Spatial periodicity
of galaxy number counts, CMB anisotropy, and SNIa Hubble diagram based on the universe
accompanied by a non-minimally coupled scalar field, Astrophys. Space Sci.
315:53, 2008. Return to text.
- This situation would also be indistinguishable from real space
structure exactly centred on our galaxy. Return to text.
- Einstein made this remark to Ernst Straus, his assistant
from about 1950–1953 at the Institute for Advanced Study at Princeton (Holton,
G., Einstein’s third paradise, Daedalus, Fall 2003, pp. 26–34;
p. 30, www.aip.org/history/einstein/essay-Einsteins-Third-Paradise.pdf, accessed
7 May 2010). Return to text.
- Hartnett, J.G., Fourier analysis of the large scale spatial
distribution of galaxies in the universe; in: Proceedings of the 2nd
Crisis in Cosmology Conference, Potter, F. (Ed.), Port Angeles, WA, ASP
Conference Series 413:77–97, 2009. Return
to text.
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