Two Tunnels to Inflation

TL;DR

This paper analyzes the tunneling processes involved in the formation of inflating bubbles in a vacuum background, comparing two mechanisms and calculating their probabilities using semi-classical methods.

Contribution

It provides a comprehensive catalog of bubble solutions with positive cosmological constants and distinguishes two tunneling mechanisms, including their probabilities.

Findings

Two distinct tunneling processes identified: wormhole-mediated and horizon-separated.

Probabilities of both mechanisms computed using WKB approximation.

Neither mechanism universally dominates across all regimes.

Abstract

We investigate the formation via tunneling of inflating (false-vacuum) bubbles in a true-vacuum background, and the reverse process. Using effective potentials from the junction condition formalism, all true- and false-vacuum bubble solutions with positive interior and exterior cosmological constant, and arbitrary mass are catalogued. We find that tunneling through the same effective potential appears to describe two distinct processes: one in which the initial and final states are separated by a wormhole (the Farhi-Guth-Guven mechanism), and one in which they are either in the same hubble volume or separated by a cosmological horizon. In the zero-mass limit, the first process corresponds to the creation of an inhomogenous universe from nothing, while the second mechanism is equivalent to the nucleation of true- or false-vacuum Coleman-De Luccia bubbles. We compute the probabilities of both mechanisms in the WKB approximation using semi-classical Hamiltonian methods, and find that -- assuming both process are allowed -- neither mechanism dominates in all regimes.