A method for testing the cosmic homogeneity with Shannon entropy

Pandey, Biswajit

doi:10.1093/mnras/stt134

Cited by 29 publications

(47 citation statements)

References 41 publications

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“…The top right panel shows the inhomogeneity 1 − Hr (Hr )max as a function of r in the LRG distribution when the analysis is carried out with overlapping spheres (Pandey 2013;Pandey et al 2015). The bottom left panel show the ratio of inhomogeneity on different length scales when measured using independent voxels and overlapping spheres.…”

Section: Results and Conclusionmentioning

confidence: 99%

“…The enormous volume covered by the SDSS LRG distribution provides us an unique opportunity to test the assumption of homogeneity on large scales with unprecedented confidence. We modify our method (Pandey 2013) so as to carry out the analysis with non-overlapping independent regions upto sufficiently large length scales. We also analyze the LRG data with overlapping spheres and compare the findings with that obtained using independent regions to asses the suppression of inhomogeneities on different length scales due to overlapping and confinement biases.…”

Section: Introductionmentioning

confidence: 99%

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Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy

Pandey

Sarkar

2016

Mon. Not. R. Astron. Soc.

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We quantify the degree of inhomogeneity in the Luminous Red Galaxy (LRG) distribution from the SDSS DR7 as a function of length scales by measuring the Shannon entropy in independent and regular cubic voxels of increasing grid sizes. We also analyze the data by carrying out measurements in overlapping spheres and find that it suppresses inhomogeneities by a factor of 5 to 10 on different length scales. Despite the differences observed in the degree of inhomogeneity both the methods show a decrease in inhomogeneity with increasing length scales which eventually settle down to a plateau at ∼ 150 h −1 Mpc. Considering the minuscule values of inhomogeneity at the plateaus and their expected variations we conclude that the LRG distribution becomes homogeneous at 150 h −1 Mpc and beyond. We also use the Kullback-Leibler divergence as an alternative measure of inhomogeneity which reaffirms our findings. We show that the method presented here can effectively capture the inhomogeneity in a truly inhomogeneous distribution at all length scales. We analyze a set of Monte Carlo simulations with certain periodicity in their spatial distributions and find periodic variations in their inhomogeneity which helps us to identify the underlying regularities present in such distributions and quantify the scale of their periodicity. We do not find any underlying regularities in the LRG distribution within the length scales probed.

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Section: Results and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy

Pandey

Sarkar

2016

Mon. Not. R. Astron. Soc.

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“…Hosoya et al 2004;Li et al 2012), extragalactic surveys (e.g. Pandey 2013;Pandey & Sarkar 2015) and compact stars (de Avellar & Horvath 2012). Crucial to these attempts is the consideration that a physical phenomenon can be treated as an information processing device, and its evolution can be studied through "word" (i.e.…”

Section: Introductionmentioning

confidence: 99%

On the complexity and the information content of cosmic structures

Vazza

2016

Mon. Not. R. Astron. Soc.

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The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to measure the information content of cosmic structure and to quantify the complexity that emerges from it, based on Information Theory. The emergence of complex evolutionary patterns is studied with a statistical symbolic analysis of the datastream produced by state-of-the-art cosmological simulations of forming galaxy clusters. This powerful approach allows us to measure how many bits of information are necessary to predict the evolution of energy fields in a statistical way, and it offers a simple way to quantify when, where and how the cosmic gas behaves in complex ways. The most complex behaviors are found in the peripheral regions of galaxy clusters, where supersonic flows drive shocks and large energy fluctuations over a few tens of million years. Describing the evolution of magnetic energy requires at least a twice as large amount of bits than for the other energy fields. When radiative cooling and feedback from galaxy formation are considered, the cosmic gas is overall found to double its degree of complexity. In the future, Cosmic Information Theory can significantly increase our understanding of the emergence of cosmic structure as it represents an innovative framework to design and analyze complex simulations of the Universe in a simple, yet powerful way.

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“…Although the polarization anisotropies are made from common curvature fluctuations, their transfer functions do not completely coincide with those of temperature anisotropies, and thus they will lend additional statistical power. Another test is to look into large-scale structure data, which offers an independent probe for primordial fluctuations [24][25][26]. The comoving scale that corresponds to the multipole range of l ≈ 213-256 is approximately k ≈ 0.015-0.018 Mpc −1 , which is at the edge of the current galaxy survey by baryon oscillation spectroscopic survey (BOSS) [27] and will be within reach in future galaxy surveys, such as Euclid [28], large synoptic survey telescope (LSST) [29], square kilometre array (SKA) [30], and others.…”

Section: Look-elsewhere Effectmentioning

confidence: 99%

Test for the zero mean hypothesis in cosmology

Ichiki

2014

Phys. Rev. D

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One working hypothesis on which analyses of cosmological data are based is the zero ensemble mean hypothesis, which is related to the statistical homogeneity of cosmological perturbations. This hypothesis, however, should be tested by observational data in the current era of precision cosmology. Herein, we test the hypothesis by analyzing recent, foreground-reduced cosmic microwave background (CMB) maps, combining the spherical harmonic coefficients of the masked CMB temperature anisotropies in such a way that the combined variables can be treated as statistically independent samples. We find evidence against the zero mean hypothesis in two particular ranges of multipoles, with significance levels of 2.5σ and 3.1σ in the multipole ranges of l ≈ 61-86 and 213-256, respectively, for both the Planck and Wilkinson Microwave Anisotropy Probe maps. The latter signal is consistent with our previous result found by using brute-force Monte Carlo simulations. However, within the method employed in this paper we conclude that the zero mean hypothesis is consistent with the current CMB data on the basis of Stouffer's weighted Z statistics, which takes multiple testing into account.

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A method for testing the cosmic homogeneity with Shannon entropy

Cited by 29 publications

References 41 publications

Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy

Probing large scale homogeneity and periodicity in the LRG distribution using Shannon entropy

On the complexity and the information content of cosmic structures

Test for the zero mean hypothesis in cosmology

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