Casimir effect in Extended Theories of Gravity

TL;DR

This paper investigates how extended theories of gravity modify the Casimir effect for a scalar field between parallel plates in a weakly curved spacetime, providing theoretical predictions for future experimental tests.

Contribution

It derives the gravity-induced corrections to Casimir energy and pressure within extended theories of gravity using a perturbative approach, generalizing results beyond general relativity.

Findings

Gravity corrections to Casimir energy are small but theoretically significant.

Future gravitational interferometers could detect these corrections.

The study provides relations to constrain parameters of extended gravity theories.

Abstract

We study the Casimir vacuum energy density and the Casimir pressure for a massless scalar field confined between two nearby parallel plates in a slightly curved, static spacetime background, employing the weak field approximation in the framework of Extended Theories of Gravity (ETG). Following a perturbative approach upto second order, we find the gravity correction in the ETG to Casimir vacuum energy density and pressure. The corrections to the vacuum energy density in presence of curved spacetime in the framework of General Relativity (GR) are small and today they are still undetected with the current technology. However, future sensitivity improvement in gravitational interferometer experiments will give an useful tool to detect such effect induced by gravity. For these reason we retain interesting from a theoretical point of view generalize the outcomes of GR in the context of ETG. Finally, we find the general relation to constraining the free parameters of the ETG.