Comparing Dark Energy models with Hubble versus Growth Rate data

TL;DR

This paper compares various dark energy models using combined growth and expansion data, employing multiple statistical criteria to evaluate model performance and introducing a 3D Figure of Merit for comprehensive analysis.

Contribution

It introduces a novel 3D Figure of Merit and systematically compares dark energy models using multiple statistical methods on combined growth and expansion data.

Findings

Different models show varying levels of support depending on the statistical criterion used.

The 3D Figure of Merit provides a more comprehensive assessment of model accuracy.

Statistical criteria can yield different rankings of models.

Abstract

In this work we perform an analysis on the recently proposed conjoined cosmic growth and cosmic expansion diagram [1] to compare several dark energy models using the Figure of Merit showed in [2], which consists in the inverse of the $1\sigma$ confidence region in the $f\sigma_8(z)-H(z)$ plot. Our analysis also consists of comparing the models by performing different statistical criteria: Bayes factor [3], the Bayesian Information Criteria [4] and the Akaike Information Criterion [5]. We also developed a 3-dimensional Figure of Merit to account simultaneously for the errors on the growth rate and the Hubble parameter. The main idea is to consider several cosmological models and compare them with the different statistical criteria in order to highlight the differences and the accuracies of each single criterion.