Vacuum transitions with the Gauss-Bonnet term in $D$ dimensions

TL;DR

This paper generalizes previous work on vacuum decay and tunneling exponents to higher dimensions with the Gauss-Bonnet term, revealing a proportionality of the Euclidean action to curvature and discovering a new decay channel from AdS to dS.

Contribution

It extends the analysis of vacuum decay to arbitrary dimensions including the Gauss-Bonnet term, and identifies a new decay channel relevant to string theory landscapes.

Findings

Euclidean action B is proportional to k_{+}^{-(D-2)}

Discovery of a new decay channel from anti-de Sitter to de Sitter

Behavior of tunneling exponent generalizes to D dimensions

Abstract

In our previous paper [1,2], we proposed a probabilistic argument to explain the reason why the cosmological constant is very small in $4D$. We can ask a question: if the behavior of tunneling exponent $B$ can be generalized to $D$-dimension. Moreover, in higher dimensional theory motivated by string theory the Gauss-Bonnet term plays an important role. Therefore, in this paper, we generalize our result in [1,2] to arbitrary $D$ dimensions including the Gauss-Bonnet term. As a result, we have two main results. We find that the Euclidean action of the bounce, $B$, describing the decay of a de Sitter vacuum, is proportional to $k^{-(D-2)}_{+}$, which has a pole as $k^2_{+} \rightarrow 0$ where $k^2_{+}$ is the curvature of the parent vacuum. This result is similar to the result in $4D$. The other result is that we find a new decay channel, describing up-tunneling from anti-de Sitter into de Sitter. The meaning of this new decay channel in the string landscape should be explored in the future.