Non-local gravity and comparison with observational datasets. II. Updated results and Bayesian model comparison with $\Lambda$CDM

TL;DR

This study compares two non-local gravity models, RR and RT, with observational cosmological data, finding that RT matches $ ext{Lambda}$CDM performance, while RR's performance varies with $H_0$ priors, using Bayesian analysis.

Contribution

The paper provides an updated, comprehensive comparison of non-local gravity models with observational data, implementing them in a Boltzmann code and performing Bayesian model comparison.

Findings

RT model performs as well as $ ext{Lambda}$CDM.

RR model's performance depends on $H_0$ prior.

Bayesian comparison favors RT over RR in some cases.

Abstract

We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the {\em Planck} 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data, isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA supernovae, $H_0$ measurements and growth rate data, and we perform Bayesian parameter estimation. We then compare the RR, RT and $\Lambda$CDM models, using the Savage-Dickey method. We find that the RT model and $\Lambda$CDM perform equally well, while the performance of the RR model with respect to $\Lambda$CDM depends on whether or not we include a prior on $H_0$ based on local measurements.