New Regularization in Extra Dimensional Model and Renormalization Group Flow of the Cosmological Constant

TL;DR

This paper introduces a new regularization method for calculating Casimir energy in a warped 5D scalar theory, revealing how the warp parameter renormalizes and impacting the cosmological constant problem.

Contribution

It proposes sphere lattice regularization for 5D warped geometries and analyzes the renormalization effects on the warp parameter and cosmological constant.

Findings

Casimir energy is finite after renormalization.

Warp parameter undergoes renormalization effects.

Implications for the cosmological constant problem.

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, warp parameter) and $T$(extra space IR 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}. We examine the cosmological constant problem.