Abstract
Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon adiabatic invariants and time modeling of a typical inflaton field which has slow and fast time variation components. A faster computation time for numerical integration is achieved via subtraction of slowly varying components that are ultimately exponentially suppressed. The fast oscillatory remnant results in production of scalar particles with a mass larger than the inflationary Hubble expansion rate through a mechanism analogous to perturbative particle scattering. An improved effective Boltzmann collision equation description of this particle production mechanism is developed. This model allows computation of the spectrum using only adiabatic invariants, avoiding the need to explicitly solve the inflaton equations of motion.
Highlights
Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation
Unlike the scenarios of refs. [27, 41,42,43], the phase space structure of the initial inflaton degrees of freedom is fixed by the Bunch-Davies/adiabatic vacuum prescription during inflation. It is in this sense that the particle production considered in ref. [8] might naively be thought of as part of the gravitational particle production resulting from the transition out of the quasi-dS era
We will find below that the quantum interference error considerations lead to a time width at an intermediate scale between those set by the inflaton mass and Hubble expansion rate, i.e. m−φ 1 ∆t(v) H−1(v)
Summary
Gravitational production of superheavy hidden sector particles during the transition out of the inflationary quasi-de Sitter (quasi-dS) era remains a plausible mechanism of dark matter production (e.g. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]). gravitational production of super-Hubble-mass particles was largely considered phenomenologically uninteresting due to an exponential suppression during inflation. This outlook has changed after it was found [8, 29, 30] that unsuppressed production can take place after inflation via coherent oscillating inflatons φ → graviton → χ particles (1.1). The adiabatic invariant formalism of this paper is used to analyze the dynamics of the inflaton φ and the scale factor a, and is controlled by H/mφ This determines the χ mode dispersion, which controls its particle production. This tool will play a crucial role, where we present a more accurate approximation of the Boltzmann equation, which is one of the main goals of this paper. The appendices include a review of the adiabatic invariant formalism used in this paper and a derivation of an explicit formula for the time dependence of the slowly varying Hubble expansion rate after the end of inflation for a generic inflationary potential
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