Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve with Shannon entropy

Pandey, Biswajit; Sarkar, Suman

doi:10.1093/mnras/stv2166

Cited by 34 publications

(39 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…Pandey et al (2015) applied this method to galaxy distributions from SDSS DR12 (Alam et al 2015) and find that the inhomogeneities in the galaxy distributions persist at least upto a length scale of 120 h −1 Mpc. Pandey (2013) show that the methods for testing homogeneity based on the number counts are contaminated by confinement and overlapping biases which result from the systematic migration and overlap between the spheres with increasing radii.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Pandey

Sarkar

2016

Mon. Not. R. Astron. Soc.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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.

Self Cite

View full text Add to dashboard Cite

show abstract

“…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.

View full text Add to dashboard Cite

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.

show abstract

“…The Cosmological Principle (CP) is considered to be the foundation of modern cosmology, stating that the Universe must be isotropic and homogeneous on sufficiently large scales. It is robustly supported by various cosmological probes such as the cosmic microwave background observed by WMAP (Bennett et al 2013) and Planck (Planck Collaboration et al 2016a) satellites, the distribution of distant radio sources (Condon 1988;Blake & Wall 2002) and the large scale distribution of galaxies (Marinoni et al 2012;Appleby & Shafieloo 2014;Alonso et al 2015;Pandey & Sarkar 2015).…”

Section: Introductionmentioning

confidence: 88%

Anisotropy of the galaxy cluster X-ray luminosity–temperature relation

Migkas

Reiprich

2018

A&A

View full text Add to dashboard Cite

We introduce a new test to study the Cosmological Principle with galaxy clusters. Galaxy clusters exhibit a tight correlation between the luminosity and temperature of the X-ray-emitting intracluster medium. While the luminosity measurement depends on cosmological parameters through the luminosity distance, the temperature determination is cosmology-independent. We exploit this property to test the isotropy of the luminosity distance over the full extragalactic sky, through the normalization a of the L X − T scaling relation and the cosmological parameters Ω m and H 0 . To this end, we use two almost independent galaxy cluster samples: the ASCA Cluster Catalog (ACC) and the XMM Cluster Survey (XCS-DR1). Interestingly enough, these two samples appear to have the same pattern for a with respect to the Galactic longitude. More specifically, we identify one sky region within l ∼ (−15 • , 90 • ) (Group A) that shares very different best-fit values for the normalization of the L X − T relation for both ACC and XCS-DR1 samples. We use the Bootstrap and Jackknife methods to assess the statistical significance of these results. We find the deviation of Group A, compared to the rest of the sky in terms of a, to be ∼ 2.7σ for ACC and ∼ 3.1σ for XCS-DR1. This tension is not significantly relieved after excluding possible outliers and is not attributed to different redshift (z), temperature (T ), or distributions of observable uncertainties. Moreover, a redshift conversion to the cosmic microwave background (CMB) frame does not have an important impact on our results. Using also the HIFLUGCS sample, we show that a possible excess of cool-core clusters in this region, is not able to explain the obtained deviations. Furthermore, we tested for a dependence of the results on supercluster environment, where the fraction of disturbed clusters might be enhanced, possibly affecting the L X − T relation. We indeed find a trend in the XCS-DR1 sample for supercluster members to be underluminous compared to field clusters. However, the fraction of supercluster members is similar in the different sky regions, so this cannot explain the observed differences, either. Constraining Ω m and H 0 via the redshift evolution of L X − T and the luminosity distance via the flux-luminosity conversion, we obtain approximately the same deviation amplitudes as for a. It is interesting that the general observed behavior of Ω m for the sky regions that coincide with the CMB dipole is similar to what was found with other cosmological probes such as supernovae Ia. The reason for this behavior remains to be identified.

show abstract

Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve with Shannon entropy

Cited by 34 publications

References 74 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

Anisotropy of the galaxy cluster X-ray luminosity–temperature relation

Contact Info

Product

Resources

About