We study the gravitational production of massive particles with mass greater or comparable to the Hubble parameter in the early universe and possible imprints left in the primordial power spectrum through interactions. We first investigate the standard WKB approach of the gravitational production problems which cannot provide a precise description for the whole production process, motivating us to develop an approximation beyond the WKB approach. By utilizing the analogy between the gravitational productions in cosmology and the quantum transitions in quantum mechanics, we follows Dingle’s asymptotic series of WKB approximation and Berry’s smoothing technique of the Stokes phenomenon to obtain an improved approximation to describe the time evolution and productions of massive p...[ Read more ]

We study the gravitational production of massive particles with mass greater or comparable to the Hubble parameter in the early universe and possible imprints left in the primordial power spectrum through interactions. We first investigate the standard WKB approach of the gravitational production problems which cannot provide a precise description for the whole production process, motivating us to develop an approximation beyond the WKB approach. By utilizing the analogy between the gravitational productions in cosmology and the quantum transitions in quantum mechanics, we follows Dingle’s asymptotic series of WKB approximation and Berry’s smoothing technique of the Stokes phenomenon to obtain an improved approximation to describe the time evolution and productions of massive particles, called the Stokes-line method. We then apply the Stokes-line method to study the gravitational productions in several cosmological scenarios in the early universe, and a toy model the smooth transition to a subsequent scenario is also analyzed with the estimation of dark matter relic abundance. After confirming the feasibility of the Stokes-line method, we also analyze the possible clock signal imprinted in the primordial power spectrum in an inflationary scenario with non-zero and slowly-changing η, the second slow-roll parameter, and the the form of the clock signal is expected to be cos(Ak^η/2 + ∅).