Renormalization Group Flow and the Dark Energy Problem

TL;DR

This paper calculates the Casimir energy in a 5D warped geometry using a novel sphere lattice regularization, explores its renormalization, and discusses implications for the dark energy problem.

Contribution

It introduces a new regularization method for 5D Casimir energy in warped geometry and analyzes its renormalization effects on the warp parameter.

Findings

5D Casimir energy is finite after renormalization.

Warp parameter undergoes renormalization effects.

Implications for dark energy are discussed.

Abstract

Casimir energy is calculated for 5D scalar theory in the {\it warped} geometry. A new regularization, called {\it sphere lattice regularization}, is taken. The regularized configuration is {\it closed-string like}. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, extra space UV-boundary parameter) and $T$(extra space IR-boundary parameter) dependence of Casimir energy. 5D Casimir energy is {\it finitely} obtained after the {\it proper renormalization procedure.} The {\it warp parameter} $\om$ suffers from the {\it renormalization effect}. Regarding Casimir energy as the main contribution to the cosmological term, we examine the dark energy problem.