Renormalized stress tensor in one-bubble spacetimes

TL;DR

This paper calculates the quantum stress tensor in spacetimes with nucleating bubbles, revealing its perfect fluid form and specific equations of state in two models involving bubble nucleation and vacuum decay.

Contribution

It provides explicit computations of the renormalized stress tensor in one-bubble spacetimes for the first time, highlighting its perfect fluid structure and asymptotic equations of state.

Findings

Stress tensor has perfect fluid form in both models.

In the Vilenkin-Ipser-Sikivie case, pressure is -1/3 of energy density.

Energy density is dominated by supercurvature mode gradients.

Abstract

We compute the two-point function and the renormalized expectation value of the stress tensor of a quantum field interacting with a nucleating bubble. Two simple models are considered. One is the massless field in the Vilenkin-Ipser-Sikivie spacetime describing the gravitational field of a reflection symmetric domain wall. The other is vacuum decay in flat spacetime where the quantum field only interacts with the tunneling field on the bubble wall. In both cases the stress tensor is of the perfect fluid form. The assymptotic form of the equation of state are given for each model. In the VIS case, we find that $p=-(1/3)\rho$, where the energy density $\rho$ is dominated by the gradients of supercurvature modes.