Non-singular bounce transitions in the multiverse

TL;DR

This paper investigates non-singular bounce transitions in the multiverse, proposing a modified Friedmann dynamics that replaces singularities with bounces, leading to vacuum transitions and potential bubble fragmentation.

Contribution

It introduces a simple model of non-singular bounces in the multiverse using a modified Friedmann equation and analyzes the resulting vacuum transition dynamics.

Findings

Bounces typically cause transitions to different vacua with scalar field displacement ~1 in Planck units.

Multiple bounces can occur until the field reaches a positive-energy de Sitter vacuum.

Perturbation amplification mechanisms are less efficient than in slow-roll inflation but may still fragment bubbles.

Abstract

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value $\rho_c$. This is combined with a simple scalar field `landscape', where the energy barriers between different vacua are small compared to $\rho_c$. We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement $\Delta\phi \sim 1$ in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.