Information entropy in cosmological inference problems

May 5, 2020
12 pages
Published in:
  • Mon.Not.Roy.Astron.Soc. 503 (2021) 1, 1187-1198
  • Published: Mar 25, 2021
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Abstract: (Oxford University Press)
The subject of this paper is a quantification of the information content of cosmological probes of the large-scale structures, specifically of temperature and polarization anisotropies in the cosmic microwave background (CMB), CMB-lensing, weak cosmic shear and galaxy clustering, in terms of information theory measures like entropies. We aim to establish relationships between conventional measures of statistical uncertainties and information entropies for Gaussian likelihoods, which are described by the Fisher-formalism. Furthermore, we extend these studies to the computation of (Bayesian) evidences and the power of measurement to distinguish between competing models. We investigate in detail how cosmological data decrease information entropy by reducing statistical errors and by breaking degeneracies. In addition, we work out how tensions between data sets increase information entropy and quantify this effect in three examples: the discrepancy in Ω_m and σ_8 between the CMB and weak lensing, the role of intrinsic alignments in weak lensing data when attempting the dark energy equation of state parameters, and the famous H_0-tension between Cepheids in the Hubble keystone project and the CMB as observed by Planck.
Note:
  • 12 pages, 5 figures, submitted to MNRAS
  • gravitational lensing: weak
  • dark energy
  • large-scale structure of Universe