Nonlocal effective action and particle creation in $D$ dimensions

TL;DR

This paper calculates the particle creation rate in curved spacetimes across various dimensions by analyzing the imaginary part of the effective action, revealing conditions under which particle creation occurs or is suppressed.

Contribution

It provides a general expression for the effective action's imaginary part in arbitrary dimensions, highlighting the role of curvature tensors and conformal flatness in particle creation.

Findings

No particle creation for conformal fields in conformally flat spacetimes up to second order in curvature.

Expressed the vacuum persistence amplitude in terms of Ricci scalar and Weyl tensor.

Identified the importance of the particle creation threshold in curved spacetime analysis.

Abstract

We compute the particle creation rate in the context of quantum fields in curved spacetimes, by evaluating the imaginary part of the effective action up to second order in the curvatures. For arbitrary metrics in dimensions $D\geq4$, we express the vacuum persistence amplitude in terms of the Ricci scalar and the Weyl tensor, showing that, up to their second power, no particle creation occurs for conformal fields in conformally flat spacetimes. We pinpoint an analogy with the electromagnetic pair creation, by writing the squared Weyl tensor invariant in terms of its electric and magnetic parts. In addition, we present an alternative expression for the imaginary part of the effective action employing the Cotton tensor. This is particularly useful in $D=3$, where the Weyl tensor trivially vanishes and the Cotton tensor is related to conformal flatness. Finally, we highlight the importance of the threshold for particle creation, a point that has been overlooked in some recent studies.