Graviton Mode Function in Inflationary Cosmology

TL;DR

This paper derives an analytic graviton mode function during inflation, compares it with numerical results, and introduces a pre-inflationary epoch to better understand graviton production and its observational signatures.

Contribution

It provides a simple analytic approximation for graviton mode functions in inflationary cosmology, including a pre-inflationary epoch, and validates it against numerical calculations.

Findings

The sudden approximation is fairly accurate for graviton mode functions.

The analytic mode function helps estimate graviton spectral energy density.

Pre-inflationary radiation epoch influences graviton production estimates.

Abstract

We consider the production of gravitons in an inflationary cosmology by approximating each epoch of change in the equation of state as sudden, from which a simple analytic graviton mode function has been derived. We use this mode function to compute the graviton spectral energy density and the tensor-induced cosmic microwave background anisotropy. The results are then compared to the numerical calculations which incorporate a smooth radiation-matter phase transition. We find that the sudden approximation is a fairly good method. Besides, in determining the frequency range and amplitude of the mode function, we introduce a pre-inflationary radiation-dominated epoch and use a physically sensible regularization method.