Gravitational Wave Signals From Early Matter Domination: Interpolating Between Fast and Slow Transitions

Upcoming gravitational wave experiments may probe cosmological gravitational wave sources, including those that indicate an early matter dominated epoch.  This signal arises at second order, produced from primordial curvature perturbations, but its spectral shape and frequency depends on the subsequent cosmological evolution.  Previous studies have indicated a resonant-like enhancement of the signal if the early matter dominated epoch ends suddenly, but conversely the signal is strongly suppressed if the early matter epoch ends slowly.

The approximations used in these studies make it difficult to interpolate between these regimes, which is necessary to determine the signal from any physically motivated scenario (such as primordial black hole or Q-ball domination).  In this work, we present the first complete analysis which uses exact expressions for the scale factor, Hubble parameter, Green's function, and related quantities during the transition period to determine the gravitational wave signal.  This allows us to study the intermediate regime and demonstrate the rate at which the resonant peak is suppressed as the transition time lengthens.