Tunneling in $\Lambda$ Decaying Cosmologies and the Cosmological Constant Problem

TL;DR

This paper calculates the tunneling rate in decaying $ ext{Lambda}$ cosmologies with a focus on the most probable cosmological constant, offering insights into the cosmological constant problem through instanton methods.

Contribution

It provides an exact calculation of tunneling rates in $ ext{Lambda}$ decaying cosmologies using the dilute-instanton approximation, highlighting the case $m=2$ as most probable.

Findings

Maximum tunneling rate at $m=2$, corresponding to cosmic string matter.

Most probable cosmological constant aligns with Strominger's proposal.

Results suggest a potential solution to the cosmological constant problem.

Abstract

The tunneling rate, with exact prefactor, is calculated to first order in $\hbar$ for an empty closed Friedmann-Robertson-Walker (FRW) universe with decaying cosmological term $\Lambda \sim R^{-m}$ ($R$ is the scale factor and $m$ is a parameter $0\leq m \leq 2$). This model is equivalent to a cosmology with the equation of state $p_{\chi}=(m/3 -1)\rho_{\chi}$. The calculations are performed by applying the dilute-instanton approximation on the corresponding Duru-Kleinert path integral. It is shown that the highest tunneling rate occurs for $m=2$ corresponding to the cosmic string matter universe. The obtained most probable cosmological term, like one obtained by Strominger, accounts for a possible solution to the cosmological constant problem.