Preheating and gravitational waves in large-field hilltop inflation

Abstract

The combined Planck, BICEP/Keck Array and BAO measurements of the scalar spectral index and the tensor-to-scalar ratio from the cosmic microwave background observations severely constrain or completely rule out several models of inflationary potentials. On the other hand, the data seems to favor concave potentials over convex ones. In this paper, we study preheating and gravitational waves after inflation in a large-field, regularized hilltop potential where inflation takes place in the concave plateau. The inflaton, $\phi$, is coupled to a subdominant scalar field, $\chi$, through a quartic coupling. After inflation ends, $\phi$ oscillates about the potential minimum and becomes inhomogeneous. The growth of the fluctuation modes, $\delta\phi_k$ and $\delta\chi_k$, in a homogeneous, oscillating background is analyzed in linear perturbation theory, revealing that small modes likely experience broad self-resonance or external parametric resonance. To determine if the resonances are sufficiently strong to cause unstable growth of the modes we perform a lattice simulation. The lattice simulations demonstrate that, although the initial inhomogeneities generate a stochastic gravitational wave background that remains below the present observational limit, the fluctuations do not grow exponentially, and the occupation numbers of $\delta\phi_k$ and $\delta\chi_k$ remain close to zero.