Cosmological constant, brane tension and large hierarchy in a generalized Randall-Sundrum braneworld scenario

TL;DR

This paper explores how a cosmological constant on the brane affects the hierarchy problem in a generalized Randall-Sundrum model, revealing bounds and tuning conditions depending on the sign of the cosmological constant.

Contribution

It extends the RS braneworld scenario to include a brane cosmological constant, analyzing its impact on hierarchy resolution and brane tension bounds.

Findings

Negative cosmological constant imposes an upper bound on its magnitude.

Positive cosmological constant allows no such bound but requires fine-tuning.

Hierarchy problem resolution relates to tuning the modulus and cosmological constant.

Abstract

We consider a generalized Randall Sundrum (RS) brane world scenario with a cosmological constant $\Omega$ induced on the visible brane. We show that for $\Omega<0$, resolution of the hierarchy problem requires an upper bound on the magnitude of $\Omega$. The corresponding tension on the visible brane can be positive or negative. On the other hand, there is no such bound for $\Omega>0$. However, in this case, the resolution of the hierarchy problem along with the tuning of the value of the cosmological constant to its observed value closed to $+10^{-124}$ (in Planck units) naturally lead to the tuning of the modulus to a small value of inverse Planck length as estimated in the original RS scenario.