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Register a new userTesting Cosmic Homogeneity Using Galaxy Clusters
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Michael J. Longo
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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.
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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.
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.
We explore voids in dark matter and halo fields from simulations of $Lambda$CDM and Hu-Sawicki $f(R)$ models. In $f(R)$ gravity, dark matter void abundances are greater than that of general relativity (GR). However, when using haloes to identify voids, the differences of void abundances become much smaller, but can still be told apart, in principle, at the 2, 6 and 14 $sigma$ level for the $f(R)$ model parameter amplitudes of $|f_{R0}|=10^{-6}$, $10^{-5}$ and $10^{-4}$. In contrast, the abundance of large voids found using haloes in $f(R)$ gravity is lower than in GR. The more efficient halo formation in underdense regions makes $f(R)$ voids less empty of haloes. This counter intuitive result suggests that voids are not necessarily emptier in $f(R)$ if one looks at galaxies in voids. Indeed, the halo number density profiles of voids are not distinguishable from GR. However, the same $f(R)$ voids are more empty of dark matter. This can in principle be observed by weak gravitational lensing of voids, for which the combination of a spec-$z$ and a photo-$z$ survey over the same sky is necessary. For a volume of 1~(Gpc/$h$)$^3$, neglecting the lensing shape noise, $|f_{R0}|=10^{-5}$ and $10^{-4}$ may be distinguished from GR using the lensing tangential shear signal around voids by 4 and 8$sigma$. The line-of-sight projection of large-scale structure is the main systematics that limits the significance of this signal, limiting the constraining power for $|f_{R0}|=10^{-6}$. The halo void abundance being smaller and the steepening of dark matter void profiles in $f(R)$ models are unique features that can be combined to break the degeneracy between $|f_{R0}|$ and $sigma_8$. The outflow of mass from void centers and velocity dispersions are greater in $f(R)$. Model differences in velocity profiles imply potential powerful constraints of the model in phase space and in redshift space.
Motivated by recent suggestions that a number of observed galaxy clusters have masses which are too high for their given redshift to occur naturally in a standard model cosmology, we use Extreme Value Statistics to construct confidence regions in the mass-redshift plane for the most extreme objects expected in the universe. We show how such a diagram not only provides a way of potentially ruling out the concordance cosmology, but also allows us to differentiate between alternative models of enhanced structure formation. We compare our theoretical prediction with observations, placing currently observed high and low redshift clusters on a mass-redshift diagram and find -- provided we consider the full sky to avoid a posteriori selection effects -- that none are in significant tension with concordance cosmology.
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