Integrated Sachs-Wolfe-galaxy cross-correlation bounds on the two branches of the minimal theory of massive gravity

TL;DR

This paper investigates how the integrated Sachs-Wolfe-galaxy cross-correlation constrains the normal branch of the minimal theory of massive gravity, showing it can fit current data well within certain parameter ranges and can be distinguished from standard cosmology in future observations.

Contribution

It provides the first detailed analysis of ISW-galaxy correlations in the normal branch of MTMG, identifying parameter regions consistent with observations and highlighting potential for future tests.

Findings

Positive cross-correlation achieved for large parameter space.

Normal branch of MTMG fits current data well within certain parameters.

Future experiments can distinguish MTMG from ΛCDM in GR.

Abstract

The minimal theory of massive gravity (MTMG) has two branches of stable cosmological solutions: a self-accelerating branch, which, except for the mass of tensor modes has exactly the same behavior of linear perturbations as $\Lambda$CDM in general relativity (GR), and a normal branch with nontrivial behavior. We explore the influence of the integrated Sachs-Wolfe-galaxy correlation constraints on the normal branch of MTMG, which, in its simplest implementation, has one free parameter more than $\Lambda$CDM in GR (or the self-accelerating branch of MTMG): $\theta$. This parameter is related to the graviton mass and only affects the behavior of the cosmological linear perturbation dynamics. Using 2d-mass and SDSS data, we check which values of $\theta$ lead to a positive or negative cross-correlation. We find that positive cross-correlation is achieved for a large parameter-space interval. Within this allowed region of parameter space, we perform a $\chi^2$ analysis in terms of the parameter $\theta$, while keeping the other background parameters fixed to the best-fit values of Planck. We then infer that the normal branch of MTMG fits the data well in a nontrivial portion of the parameter space, and future experiments should be able to distinguish such a model from $\Lambda$CDM in GR (or the self-accelerating branch of MTMG).