One-Loop Effective Action on Rotational Spacetime: Zeta-Function Regularization and Schwinger Perturbative Expansion

TL;DR

This paper uses zeta-function regularization and Schwinger perturbation to compute the effective action of a scalar field in a rotating cosmological spacetime, revealing quantum effects that damp early universe rotation.

Contribution

It provides an analytic form of the effective action for a rotating spacetime up to second order in rotation, using zeta-function regularization and Schwinger expansion.

Findings

Quantum effects can damp cosmological rotation in the early universe.

Analytic expression for the effective action in a perturbed rotating spacetime.

Demonstrates the impact of quantum fields on cosmological rotational dynamics.

Abstract

The zeta-function regularization method is used to evaluate the renormalized effective action for massless conformally coupling scalar field propagating in a closed Friedman spacetime perturbed by a small rotation. To the second order of the rotational parameter in the model spacetime the analytic form of the effective action is obtained with the help of the Schwinger perturbation formula. After investigating the time evolution of the rotational parameter we find that the quantum field effect can produce an effect which damps the cosmological rotational in the early universe.