We study the evolution of Gravitational Waves (GWs) during and after inflation as well as the resulting observational consequences in a Lorentz-violating massive gravity theory with one scalar (inflaton) and two tensor degrees of freedom. We consider two explicit examples of the tensor mass $m_g$ that depends either on the inflaton field $phi$ or on its time derivative $dot{phi}$, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinskys $R^2$ inflation model with a $phi$-dependent $m_g$ and the second is a low-energy-scale inflation model with a $dot{phi}$-dependent $m_g$. We compute the energy density spectrum $Omega_{rm GW}(k)$ today of the GW background. In the Starobinskys model, we show that the GWs can be amplified up to the detectable ranges of both CMB and DECIGO, but the bound from the big bang nucleosynthesis is quite tight to limit the growth. In low-scale inflation with a fast transition to the reheating stage driven by the potential $V(phi)=M^2 phi^2/2$ around $phi approx M_{rm pl}$ (where $M_{rm pl}$ is the reduced Planck mass), we find that the peak position of $Omega_{rm GW}(k)$ induced by the parametric resonance can reach the sensitivity region of advanced LIGO for the Hubble parameter of order 1 GeV at the end of inflation. Thus, our massive gravity scenario offers exciting possibilities for probing the physics of primordial GWs at various different frequencies.
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