Casimir Effect in the Horava-Lifshitz Gravity with a Cosmological Constant

TL;DR

This paper investigates how the Casimir energy of a scalar field is affected by Hořava-Lifshitz gravity with a cosmological constant, revealing modifications in weak-field approximations.

Contribution

It provides the first analysis of the Casimir effect within Hořava-Lifshitz gravity considering a cosmological constant in weak-field regimes.

Findings

Casimir energy is modified by HL gravity parameters.

Cosmological constant influences the Casimir energy.

Second order weak-field approximation shows measurable effects.

Abstract

We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R. To this end, we take into account a static and spherically symmetric solution of Ho\v{r}ava-Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.