THESIS
2020
x, 46 pages : color illustrations ; 30 cm
Abstract
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...[
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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 + ∅).
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