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We study Gravitational Waves (GWs) in the context of Massive Gravity, anextension to General Relativity (GR) where the fluctuations of the metric havea nonzero mass, and specifically investigate the effect of the tensor modes onthe Cosmic Microwave Background (CMB) anisotropies. We first study the timeevolution of the tensor modes in Massive Gravity and show that there is agraviton 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 indistinguishablefrom the corresponding ones in GR. Also, we show that short wavelength massivemodes behave almost indistinguishably from their massless counterparts. Lateron, 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 thelower multipoles ($\ell< 30$) in the CMB anisotropy power spectrum. Hence, ourresults show that CMB anisotropies measurements might be decisive to showwhether the tensor modes are massive or not.

CMB anisotropies induced by tensor modes in Massive Gravity