Stabilizing the gravitational action and Coleman's solution to the cosmological constant problem

TL;DR

This paper applies a 5-th time action formalism to stabilize Euclidean 4-D gravity in minisuperspace models, demonstrating that quantum corrections preserve the Coleman solution and address the cosmological constant problem.

Contribution

It introduces a novel application of the 5-th time action formalism to stabilize gravity models and analyze quantum effects on the cosmological constant.

Findings

Semiclassical solutions include the $S^4$ and Coleman peak at zero cosmological constant.

Scalar gravitational modes contribute positively at one-loop, removing phase ambiguity.

The approach stabilizes Euclidean gravity in simplified models.

Abstract

We use the 5-th time action formalism introduced by Halpern and Greensite to stabilize the unbounded Euclidean 4-D gravity in two simple minisuperspace models. In particular, we show that, at the semiclassical level ($\hbar \rightarrow 0$), we still have as a leading saddle point the $S^4$ solution and the Coleman peak at zero cosmological constant, for a fixed De Witt supermetric. At the quantum (one-loop) level the scalar gravitational modes give a positive semi-definite Hessian contribution to the 5-D partition function, thus removing the Polchinski phase ambiguity.