A Completely Regular Quantum Stress Tensor with $w < -1$

TL;DR

This paper confirms that adjusting the initial quantum state can eliminate divergences and redshifting issues in the two-loop stress tensor calculations for a scalar field in de Sitter space, improving cosmological quantum field theory methods.

Contribution

It verifies a 2004 conjecture that initial state corrections can absorb divergences and redshifting terms in two-loop stress tensor computations in de Sitter space.

Findings

Initial state corrections absorb divergences.

Redshifting terms are effectively managed.

Method improves quantum field computations in cosmology.

Abstract

For many quantum field theory computations in cosmology it is not possible to use the flat space trick of obtaining full, interacting states by evolving free states over infinite times. State wave functionals must be specified at finite times and, although the free states suffice to obtain the lowest order effects, higher order corrections necessarily involve changes of the initial state. Failing to correctly change the initial state can result in effective field equations which diverge on the initial value surface, or which contain tedious sums of terms that redshift like inverse powers of the scale factor. In this paper we verify a conjecture from 2004 that the lowest order initial state correction can indeed absorb the initial value divergences and all the redshifting terms of the two loop expectation value of the stress tensor of a massless, minimally coupled scalar with a quartic self interaction on nondynamical de Sitter background.