Calculation of density fluctuation in inflationary epoch

TL;DR

This paper derives an expression for quantum energy density fluctuations during inflation starting from a thermal initial state, showing the initial state's effects are negligible and emphasizing the importance of evaluating fluctuations at the Hubble crossing.

Contribution

It provides a new derivation of density fluctuations considering thermal initial conditions, challenging the assumption that initial states are always washed out.

Findings

Initial thermal state effects are negligible in density fluctuations.

Quantum fluctuations should be evaluated at Hubble crossing, not later.

Standard vacuum assumptions are validated by numerical analysis.

Abstract

Starting from an initial state of thermal equilibrium, we derive an expression for the quantum fluctuation in the energy density during the inflationary epoch in terms of the mode functions for the inflaton field. The effect of this particular initial state is not washed out in the final formula, contrary to what is usually believed. Numerically, however, the effect is completely negligible, validating the use of the two point function in the vacuum state. We also point out the requirement of conventional quantum field theory during inflation, that the quantum fluctuation in a wavelength must be evaluated, at the latest, when the wavelength crosses the Hubble length, in contrast to the usual practice in the literature.