Homogeneous Instantons in Bigravity

TL;DR

This paper investigates homogeneous Hawking-Moss instantons in bigravity, deriving corrections to GR, analyzing their behavior in the dRGT limit, and discussing implications for quantum tunneling and the no-boundary proposal.

Contribution

It provides a closed-form correction to GR for HM instantons in bigravity and examines their behavior in the dRGT limit, revealing potential issues in the reduction process.

Findings

Tunneling through the self-accelerating branch is exponentially suppressed.

Probability of tunneling becomes zero in the dRGT limit.

Reduction from bigravity to dRGT massive gravity may be ill-defined.

Abstract

We study homogeneous gravitational instantons, conventionally called the Hawking-Moss (HM) instantons, in bigravity theory. The HM instantons describe the amplitude of quantum tunneling from a false vacuum to the true vacuum. Corrections to General Relativity (GR) are found in a closed form. Using the result, we discuss the following two issues: reduction to the de Rham-Gabadadze-Tolley (dRGT) massive gravity and the possibility of preference for a large $e$-folding number in the context of the Hartle-Hawking (HH) no-boundary proposal. In particular, concerning the dRGT limit, it is found that the tunneling through the so-called self-accelerating branch is exponentially suppressed relative to the normal branch, and the probability becomes zero in the dRGT limit. As far as HM instantons are concerned, this could imply that the reduction from bigravity to the dRGT massive gravity is ill-defined.