Thermal Conditions for Scalar Bosons in a Curved Space Time

TL;DR

This paper explores the thermal conditions under which scalar bosons in curved spacetime exhibit a Planckian distribution, linking vacuum expectations to statistical averages at specific temperatures, especially in radiation-dominated models.

Contribution

It provides criteria for when the vacuum expectation value of the energy-momentum tensor can be treated as a thermal average in curved spacetime.

Findings

Conditions for statistical interpretation of vacuum energy-momentum tensor

Derivation of Planckian distribution for field modes

Temperature dependence matching radiation-dominated models

Abstract

The conditions that allow us to consider the vacuum expectation value of the energy-momentum tensor as a statistical average, at some particular temperature, are given. When the mean value of created particles is stationary, a planckian distribution for the field modes is obtained. In the massless approximation, the temperature dependence is as that corresponding to a radiation dominated Friedmann-like model.