Scalar potential from de Sitter brane in 5D and effective cosmological constant

TL;DR

This paper derives the scalar potential for a de Sitter brane in five dimensions, revealing how the bulk cosmological constant influences the potential's shape and stability, with implications for the effective cosmological constant.

Contribution

It provides an explicit form of the scalar potential in the effective action for different bulk cosmological constants, highlighting stability features and the impact on the brane's cosmology.

Findings

For $\Lambda=0$ and $\Lambda>0$, the potential has an unstable maximum at the origin and vanishes at large scalar field.

For $\Lambda<0$, the potential has an unstable maximum and a stable minimum, reducing the effective cosmological constant.

Negative potential energy at the minimum can lower the brane's positive cosmological constant.

Abstract

We derive the scalar potential in zero mode effective action arising from a de Sitter brane embedded in five dimensions with bulk cosmological constant $\Lambda$. The scalar potential for a scalar field canonically normalized is given by the sum of exponential potentials. In the case of $\Lambda=0$ and $\Lambda>0$, we point out that the scalar potential has an unstable local maximum at the origin and exponentially vanishes for large positive scalar field. In the case of $\Lambda<0$, the scalar potential has an unstable local maximum at the origin and a stable local minimum, it is shown that the positive cosmological constant in brane is reduced by negative potential energy of scalar at minimum.