Observational signatures of the parametric amplification of gravitational waves during reheating after inflation

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 mg that depends either on the inflaton field φ or on its time derivative φ, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinsky's R2 inflation model with a φ-dependent mg, and the second is a low energy-scale inflation model with a φ-dependent mg. We compute the energy density spectrum ΩGW(k) today of the GW background. In the Starobinsky's model, we show that the GWs can be amplified up to the detectable ranges of both cosmic microwave background and DECi-hertz Interferometer Gravitational wave Observatory, 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(φ)=M2φ2/2 around φ≈Mpl (where Mpl is the reduced Planck mass), we find that the peak position of ΩGW(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.