Production of gravitational waves during preheating in α -attractor inflation

Abstract

We study the generation of gravitational waves (GWs) during the single-field preheating in the $\ensuremath{\alpha}$-attractor inflation in this paper. We find that the oscillation of the inflaton leads to an intermittent tachyonic instability for certain inflaton fluctuations, which results in that the inflaton quanta become a significant source of GWs. At the beginning of the preheating, the low frequency GW modes grow rapidly, and then nonlinear effects set in and lead to the growth of modes with relatively high frequencies. When the model parameter $\ensuremath{\alpha}$ is chosen to be very small, e.g., ${10}^{\ensuremath{-}5}$, the GW density spectrum increases very fast and the value of model parameter $n$ has negligible effect. However, when $\ensuremath{\alpha}$ becomes relatively large, e.g., ${10}^{\ensuremath{-}4}$ or ${10}^{\ensuremath{-}3}$, the growth of inflaton quanta is inversely proportional to the value of $n$ since a smaller value of $n$ corresponds to a more negative value of the mass square of the inflaton. This effect leads to that the maximum value of the today's total energy density of GWs occurs at $n=1$ and $\ensuremath{\alpha}={10}^{\ensuremath{-}4}$ among different values of model parameters considered in our analysis. Furthermore, we find that the GWs produced during the single-field preheating in the $\ensuremath{\alpha}$-attractor inflation satisfy the constraints from the Planck and those expected from the next-generation CMB experiments.