Cosmological parameter inference with Bayesian statistics

Abstract

Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the $\Lambda$CDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.

30 pages, 17 figures, 5 tables; accepted for publication in Universe; references added

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• Model selection applied to reconstructions of the Dark Energy
• Smoothing the $H_0$ tension with a dynamical dark energy model
• Neural network reconstructions for the Hubble parameter, growth rate and distance modulus
• Observational cosmology with Artificial Neural Networks
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• Testing an oscillatory behavior of dark energy
• Cosmological constraints on the Multi Scalar Field Dark Matter model
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• Coupled Multi Scalar Field Dark Energy
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• Constraining $\Lambda$CDM cosmological parameters with Einstein Telescope mock data
• Constraints on Power Law and Exponential models in $f(Q)$ Gravity
• Cosmography from well-localized Fast Radio Bursts
• f(R) Gravity in an Ellipsoidal Universe
• Search for the $f(R,T)$ gravity functional form via gaussian processes
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• The Lambert $W$ equation of state in light of DESI BAO
• Background-level reconstruction of scalar-field potentials from dark-energy histories and comparison with analytic potential families
• Cosmological test of a length-preserving biconnection gravity
• How Holographic is the Dark Energy? A Spline Nodal reconstruction approach