Note on the pragmatic mode-sum regularization method: translational-splitting in a cosmological background

TL;DR

This paper demonstrates that the pragmatic mode-sum regularization method for quantum fields in curved spacetime simplifies to the adiabatic regularization method in homogeneous expanding universes, connecting two approaches in quantum field theory.

Contribution

It shows that the pragmatic regularization method reduces to adiabatic regularization in backgrounds with three-dimensional spatial symmetries, unifying different renormalization techniques.

Findings

The method simplifies to adiabatic regularization in homogeneous universes.

It extends the pragmatic mode-sum regularization to cosmological backgrounds.

Provides a unified view of regularization techniques in curved spacetime.

Abstract

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization method.