Gravitational wave signatures of post-fragmentation reheating

After cosmic inflation, coherent oscillations of the inflaton field about a monomial potential $V(\phi)\sim \phi^k$ result in an expansion phase characterized by a stiff equation-of-state $w\simeq(k-2)/(k+2)$. Sourced by the oscillating inflaton condensate, parametric (self)resonant effects can induce the exponential growth of inhomogeneities eventually backreacting and leading to the fragmentation of the condensate. In this work, we investigate realizations of inflation giving rise to such dynamics, assuming an inflaton weakly coupled to its decay products. As a result, the transition to a radiation-dominated universe, i.e. reheating, occurs after fragmentation. We estimate the consequences on the production of gravitational waves by computing the contribution induced by the stiff equation-of-state era in addition to the signal generated by the fragmentation process for $k=4,6,8,10$. We find that the signal generated during the fragmentation process gives a larger contribution than the one induced by the stiff equation-of-state era in given frequency ranges for all values of $k$. Our results are independent of the reheating temperature provided that reheating is achieved posterior to fragmentation. Our work shows that the dynamics of such weakly-coupled inflaton scenario can actually result in characteristic gravitational wave spectra with frequencies from Hz to GHz, in the reach of future gravitational wave observatories, in addition to the complementarity between upcoming detectors in discriminating (post)inflation scenarios. We advocate the need of developing high-frequency gravitational wave detectors to gain insight into the dynamics of inflation and reheating.