Cosmic expansion history from SNe Ia data via information field theory: the charm code

¹ University of Barcelona, Departament de Física Quàntica i Astrofísica, Martí i Franquès 1, 08028 Barcelona, Spain
e-mail: natalia_porqueres@hotmail.com
² Max-Planck-Insitut für Astrophysik (MPA), Karl-Schwarzschild-Strasse 1, 85741 Garching, Germany
³ Institut de Ciències del Cosmos, Martí i Franquès 1, 08028 Barcelona, Spain
⁴ Instituto de Física Fundamental, CSIC, Serrano 121, 28006 Madrid, Spain

Received: 13 August 2016
Accepted: 3 December 2016

Abstract

We present charm (cosmic history agnostic reconstruction method), a novel inference algorithm that reconstructs the cosmic expansion history as encoded in the Hubble parameter H(z) from SNe Ia data. The novelty of the approach lies in the usage of information field theory, a statistical field theory that is very well suited for the construction of optimal signal recovery algorithms. The charm algorithm infers non-parametrically s(a) = ln(ρ(a) /ρ_crit0), the density evolution which determines H(z), without assuming an analytical form of ρ(a) but only its smoothness with the scale factor a = (1 + z)^-1. The inference problem of recovering the signal s(a) from the data is formulated in a fully Bayesian way. In detail, we have rewritten the signal as the sum of a background cosmology and a perturbation. This allows us to determine the maximum a posteriory estimate of the signal by an iterative Wiener filter method. Applying charm to the Union2.1 supernova compilation, we have recovered a cosmic expansion history that is fully compatible with the standard ΛCDM cosmological expansion history with parameter values consistent with the results of the Planck mission.