CMB anisotropies induced by tensor modes in Massive Gravity

TL;DR

This paper investigates how massive gravitons in Massive Gravity theories influence CMB anisotropies, identifying a mass threshold below which tensor modes mimic those in General Relativity and highlighting potential observational signatures in the CMB spectrum.

Contribution

It demonstrates the conditions under which tensor modes in Massive Gravity differ from GR and predicts observable effects on the CMB anisotropy spectrum for certain graviton masses.

Findings

Tensor modes are indistinguishable from GR for masses below 10^{-66}g.

Massive gravitons with masses around 10^{-27} to 10^{-26}cm^{-1} affect low multipoles in the CMB.

CMB measurements could potentially detect or constrain graviton mass.

Abstract

We study Gravitational Waves (GWs) in the context of Massive Gravity, an extension to General Relativity (GR) where the fluctuations of the metric have a nonzero mass, and specifically investigate the effect of the tensor modes on the Cosmic Microwave Background (CMB) anisotropies. We first study the time evolution of the tensor modes in Massive Gravity and show that there is a graviton mass limit $m_l=10^{-66}g\sim 10^{-29}cm^{-1}$, so that for masses $m\leq m_l$ the tensor perturbations in Massive Gravity are indistinguishable from the corresponding ones in GR. Also, we show that short wavelength massive modes behave almost indistinguishably from their massless counterparts. Later on, we show that massive gravitons with masses within the range $m= 10^{-27}cm^{-1}$ - $m=10^{-26}cm^{-1}$ would leave a clear signature on the lower multipoles ($\ell< 30$) in the CMB anisotropy power spectrum. Hence, our results show that CMB anisotropies measurements might be decisive to show whether the tensor modes are massive or not.