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Register a new userTesting cosmic homogeneity and isotropy using galaxy correlations
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Michael J. Longo
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Despite its fundamental importance in cosmology, there have been very few straight-forward tests of the cosmological principle. Such tests are especially timely because of the hemispherical asymmetry in the cosmic microwave background recently observed by the Planck collaboration. Most tests to date looked at the redshift dependence of cosmological parameters. These are subject to large systematic effects that require modeling and bias corrections. Unlike previous tests, the tests described here compare galaxy distributions in equal volumes at the same redshift z. This allows a straight-forward test and z-dependent biases are not a problem. Using ~10^6 galaxies from the SDSS DR7 survey, I show that re- gions of space separated by ~2 Gpc have the same average galaxy correlation radii, amplitudes, and number density to within approx. 5%, which is consistent with standard model expectations.
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According to the cosmological principle, galaxy cluster sizes and cluster densities, when averaged over sufficiently large volumes of space, are expected to be constant everywhere, except for a slow variation with look-back time (redshift). Thus, average cluster sizes or correlation lengths provide a means of testing for homogeneity that is almost free of selection biases. Using ~10^6 galaxies from the SDSS DR7 survey, I show that regions of space separated by ~2 Gpc/h have the same average cluster size and density to 5 - 10 percent. I show that the average cluster size, averaged over many galaxies, remains constant to less than 10 percent from small redshifts out to redshifts of 0.25. The evolution of the cluster sizes with increasing redshift gives fair agreement when the same analysis is applied to the Millennium Simulation. However, the MS does not replicate the increase in cluster amplitudes with redshift seen in the SDSS data. This increase is shown to be caused by the changing composition of the SDSS sample with increasing redshifts. There is no evidence to support a model that attributes the SN Ia dimming to our happening to live in a large, nearly spherical void.
We analyse the distribution of position angles of 1 million galaxies from the Hyperleda catalogue, a sample that presents the galaxies coordinates in the celestial sphere, information that allows us to look for a possible privileged direction. Our analysis involves different tests and statistical methods, from which it is possible to infer with high probability ($p$-value extremely low) that the galactic planes are not randomly oriented in the sky. Whether this is an evidence of a cosmological anisotropy or an observational bias due to local effects is something deserving further studies.
We apply our symmetry based Power tensor technique to test conformity of PLANCK Polarization maps with statistical isotropy. On a wide range of angular scales (l=40-150), our preliminary analysis detects many statistically anisotropic multipoles in foreground cleaned full sky PLANCK polarization maps viz., COMMANDER and NILC. We also study the effect of residual foregrounds that may still be present in the galactic plane using both common UPB77 polarization mask, as well as the individual component separation method specific polarization masks. However some of the statistically anisotropic modes still persist, albeit significantly in NILC map. We further probed the data for any coherent alignments across multipoles in several bins from the chosen multipole range.
We analyze a set of volume limited sample of galaxies from the SDSS to study the issue of cosmic homogeneity. We use the Renyi entropy of different order to probe the inhomogeneties present in the galaxy distributions. We also calculate the Renyi diveregence to quantify the deviations of the galaxy distribution from a homogeneous Poisson distribution on different length scales. We separately carry out the analysis using the overlapping spheres and the independent voxels. Our analysis suggests that the scale of homogeneity is underestimated in the smaller galaxy samples due to the suppression of inhomogeneities by the overlapping of the measuring speheres. We find that an analysis with the independent voxels and/or use of a significantly larger galaxy sample can help to circumvent or mitigate this problem. Combining the results from these analyses, we find that the galaxy distribution in the SDSS becomes homogeneous on a length scale beyond $140 , h^{-1}, {rm Mpc}$.
In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, $3 h^{-3} mathrm{Gpc}^3$ at $0.43 leq z leq 0.7$. We study the scaled counts-in-spheres, $mathcal{N}(<r)$, and the fractal correlation dimension, $mathcal{D}_2(r)$, to assess the homogeneity scale of the universe using a $Landy & Szalay$ inspired estimator. Defining the scale of transition to homogeneity as the scale at which $mathcal{D}_2(r)$ reaches 3 within $1%$, i.e. $mathcal{D}_2(r)>2.97$ for $r>mathcal{R}_H$, we find $mathcal{R}_H = (63.3pm0.7) h^{-1} mathrm{Mpc}$, in agreement at the percentage level with the predictions of the $Lambda$CDM model $mathcal{R}_H=62.0 h^{-1} mathrm{Mpc}$. Thanks to the large cosmic depth of the survey, we investigate the redshift evolution of the transition to homogeneity scale and find agreement with the $Lambda$CDM prediction. Finally, we find that $mathcal{D}_2$ is compatible with $3$ at scales larger than $300 h^{-1} $Mpc in all redshift bins. These results consolidate the Cosmological Principle and represent a precise consistency test of the $Lambda CDM$ model.
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