Effect of model-dependent covariance matrix for studying Baryon Acoustic Oscillations

TL;DR

This study investigates whether using a model-dependent covariance matrix in BAO analysis significantly affects cosmological parameter constraints, finding only marginal differences for current and future galaxy surveys.

Contribution

It introduces a new method to generate model-dependent covariance matrices using lognormal realizations for BAO studies.

Findings

Model-dependent covariance matrices cause only small changes in parameter constraints.

The modeling error can be approximated by increasing the confidence intervals by about 30%.

The impact is marginal for both current and upcoming galaxy surveys.

Abstract

Large-scale structures in the Universe are a powerful tool to test cosmological models and constrain cosmological parameters. A particular feature of interest comes from Baryon Acoustic Oscillations (BAOs), which are sound waves traveling in the hot plasma of the early Universe that stopped at the recombination time. This feature can be observed as a localized bump in the correlation function at the scale of the sound horizon $r_s$. As such, it provides a standard ruler and a lot of constraining power in the correlation function analysis of galaxy surveys. Moreover the detection of BAOs at the expected scale gives a strong support to cosmological models. Both of these studies (BAO detection and parameter constraints) rely on a statistical modeling of the measured correlation function $\hat{\xi}$. Usually $\hat{\xi}$ is assumed to be gaussian, with a mean $\xi_\theta$ depending on the cosmological model and a covariance matrix $C$ generally approximated as a constant (i.e. independent of the model). In this article we study whether a realistic model-dependent $C_\theta$ changes the results of cosmological parameter constraints compared to the approximation of a constant covariance matrix $C$. For this purpose, we use a new procedure to generate lognormal realizations of the Luminous Red Galaxies sample of the Sloan Digital Sky Survey Data Release 7 to obtain a model-dependent $C_\theta$ in a reasonable time. The approximation of $C_\theta$ as a constant creates small changes in the cosmological parameter constraints on our sample. We quantify this modeling error using a lot of simulations and find that it only has a marginal influence on cosmological parameter constraints for current and next-generation galaxy surveys. It can be approximately taken into account by extending the $1\sigma$ intervals by a factor $\approx 1.3$.