Semiclassical corrections to the Einstein equation and Induced Matter Theory

TL;DR

This paper explores how quantum corrections to Einstein's equations can be derived from classical fluctuations in a brane-world model, linking semiclassical gravity with induced matter theory.

Contribution

It demonstrates that local quantum corrections in a conformally flat background can be obtained via the Induced Matter Theory using the FRW metric.

Findings

Classical brane fluctuations relate to quantum corrections in Einstein's equations.

Induced Einstein equations on perturbed branes match semiclassical Einstein equations.

Quantum effects can be modeled through classical brane perturbations.

Abstract

The induced Einstein equation on a perturbed brane in the Induced Matter Theory is re-analyzed. We indicate that in a conformally flat background, the local quantum corrections to the Einstein equation can be obtained via the IMT. Using the FRW metric as the 4D gravitational model, we show that the classical fluctuations of the brane may be related to the quantum corrections to the classical Einstein equation. In other words, the induced Einstein equation on the perturbed brane correspond with the semiclassical Einstein equation.