A method for testing the cosmic homogeneity with Shannon entropy

We propose a method for testing cosmic homogeneity based on the Shannon entropy in Information theory and test the potentials and limitations of the method on Monte Carlo simulations of some homogeneous and inhomogeneous 3D point process in a finite region of space. We analyze a set of N-body simulations to investigate the prospect of determining the scale of homogeneity with the proposed method and show that the method could serve as an efficient tool for the study of homogeneity.Comment: 7 pages, 3 figures, Accepted for publication in MNRA

Does information entropy play a role in the expansion and acceleration of the Universe?

We propose an interpretation of the expansion and acceleration of the Universe from an information theoretic viewpoint. We obtain the time evolution of the configuration entropy of the mass distribution in a static Universe and show that the process of gravitational instability leads to a rapid dissipation of configuration entropy during the growth of the density fluctuations making such a Universe entropically unfavourable. We find that in an expanding Universe, the configuration entropy rate is governed by the expansion rate of the Universe and the growth rate of density fluctuations. The configuration entropy rate becomes smaller but still remains negative in a matter dominated Universe and eventually becomes zero at some future time in a $\Lambda$ dominated Universe. The configuration entropy may have a connection to the dark energy and possibly plays a driving role in the current accelerating expansion of the Universe leading the Universe to its maximum entropy configuration.Comment: 4 pages, no figures, minor revision, Accepted for publication in MNRAS Letter

Modeling non-linear effects in the redshift space two-point correlation function and its implications for the pairwise velocity dispersion

The anisotropies in the galaxy two-point correlation function measured from redshift surveys exhibits deviations from the predictions of the linear theory of redshift space distortion on scales as large 20 Mpc/h where we expect linear theory to hold in real space. Any attempt at analyzing the anisotropies in the redshift correlation function and determining the linear distortion parameter \beta requires these deviations to be correctly modeled and taken into account. These deviations are usually attributed to galaxy random motions and these are incorporated in the analysis through a phenomenological model where the linear redshift correlation is convolved with the random pairwise velocity distribution function along the line of sight. We show that a substantial part of the deviations arise from non-linear effects in the mapping from real to redshift space caused by the coherent flows. Models which incorporate this effect provide a better fit to N-body results as compared to the phenomenological model which has only the effect of random motions. We find that the pairwise velocity dispersion predicted by all the models that we have considered are in excess of the values determined directly from the N-body simulations. This indicates a shortcoming in our understanding of the statistical properties of peculiar velocities and their relation to redshift distortion.Comment: Minor Revisions, Accepted to MNRA