Einstein-Langevin Equations from Running Coupling Constants

TL;DR

This paper derives Einstein-Langevin equations incorporating quantum matter backreaction, showing that for massless fields, these equations depend solely on the theory's running coupling constants.

Contribution

It provides a derivation of Einstein-Langevin equations to lowest order, linking them explicitly to running coupling constants for massless quantum fields.

Findings

Equations are derived to lowest order in curvature expansion.

For massless fields, equations depend only on running coupling constants.

The approach clarifies the role of quantum corrections in gravitational backreaction.

Abstract

The Einstein-Langevin equations take into account the backreaction of quantum matter fields on the background geometry. We present a derivation of these equations to lowest order in a covariant expansion in powers of the curvature. For massless fields, the equations are completely determined by the running coupling constants of the theory.