Cosmological constant problem in a scenario with compactifications (RS-I model)

TL;DR

This paper explores how the Randall-Sundrum model with extra dimensions can address the cosmological constant problem by controlling vacuum energy divergences, proposing a potential solution involving compactification and brane effects.

Contribution

It applies the RS model to the cosmological constant problem, showing that compactification can potentially resolve the discrepancy between theory and observation.

Findings

The CC problem can be addressed via extra-dimensional compactification.

The compactification radius is approximately twice that used for the hierarchy problem.

Potential deviations from inverse square law of gravity could be observed at certain scales.

Abstract

In this letter, we apply the Randall-Sundrum (RS) model, a scenario based on compactifications, to control the UV divergence of the zero-point energy density equation for the vacuum fluctuations, which has been unsuccessfully addressed to the cosmological constant (CC) due to a heavy discrepancy between theory and observation. Historically, the problem of CC has been shelved in the RS point of view, having few or non literature on the subject. In this sense and as done with the hierarchy problem, we apply the RS model to solve this difference via extra dimensions; we also describe how brane effects could be the solution to this substantial difference. It should be noticed that this problem is studied assuming first Minkoswki type branes, and then followed by cosmologically more realistic FLRW type branes. We finally find some remarkably interesting consequences in the RS scenario: The CC problem can be solved via compactification of the extra dimension and the compactification radius turns out to be approximately twice the one used to solve the hierarchy problem in the $\beta\pi r$ factor by Randall and Sundrum, suggesting that this subtle difference in both problems could be caused by corrections that comes from quantum gravity effects. We also estimate the corresponding scale where, according to this results, we should begin to notice subtle deviations to the inverse square law of gravitation due to the presence of the extra dimension.