  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.
