Quantum Evolution of Inhomogeneities in Curved Space

TL;DR

This paper derives renormalized equations for matter and semi-classical gravity in inhomogeneous curved spacetime, using a Gaussian approximation to analyze the quantum evolution of the bbb4 model, demonstrating its renormalizability and finite energy-momentum tensor.

Contribution

It introduces a non-perturbative Gaussian approximation method for inhomogeneous curved spacetime, establishing its renormalizability and finiteness of the energy-momentum tensor.

Findings

Renormalized equations of motion for matter and gravity in inhomogeneous spacetime.

Demonstration of the renormalizability of the Gaussian approximation.

Finite energy-momentum tensor without additional geometrical counter-terms.

Abstract

We obtain the renormalized equations of motion for matter and semi-classical gravity in an inhomogeneous space-time. We use the functional Schrodinger picture and a simple Gaussian approximation to analyze the time evolution of the $\lambda\phi^4$ model, and we establish the renormalizability of this non-perturbative approximation. We also show that the energy-momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations, without the need of further geometrical counter-terms.