Stochastic gravitational wave from graviton bremsstrahlung in inflaton decay into massive spin 3/2 particles

The detection of primordial gravitational waves would offer a direct evidence of inflation and valuable insights into the dynamics of the early universe. During post-inflation reheating period, when the inflaton coherently oscillates at the bottom of its potential, primordial stochastic gravitational waves may be sourced by its perturbative decay into particles of different spins. Assuming the behavior of the potential near the minimum as a polynomial $V(\phi)\sim \phi^k$, where $k\ge 2$, and treating the inflaton as coherently oscillating classical field, we calculate the decay of inflaton into a pair of spin $3/2$ particles accompanied by graviton emission. We numerically study the reheating dynamics and calculate the stochastic gravitational wave spectra. Our analysis shows that the gravitational wave spectra can offer insights into the microscopic physics during inflation.