The Power Spectrum of Density Perturbations in Chain Inflation

TL;DR

This paper analyzes the density perturbations in chain inflation, showing it can produce a power spectrum consistent with observations, and explores the implications for quantum gravity and axion models.

Contribution

It provides the first detailed calculation of the scalar power spectrum in chain inflation and introduces new analytic estimates for tunneling rates beyond the thin-wall approximation.

Findings

Requires about 10^4 phase transitions per e-fold to match CMB data.

Chain inflation's perturbations imply highly unstable de Sitter spaces.

Sets an upper limit of ~10^10 GeV on the axion decay constant.

Abstract

Chain Inflation is an alternative to slow roll inflation in which the universe undergoes a series of transitions between different vacua. The density perturbations (studied in this paper) are seeded by the probabilistic nature of tunneling rather than quantum fluctuations of the inflaton. We find the scalar power spectrum of chain inflation and show that it is fully consistent with a $\Lambda$CDM cosmology. In agreement with some of the previous literature (and disagreement with others), we show that $10^4$ phase transitions per e-fold are required in order to agree with the amplitude of Cosmic Microwave Background anisotropies within the observed range of scales. Interestingly, the amplitude of perturbations constrains chain inflation to a regime of highly unstable de Sitter spaces, which may be favorable from a quantum gravity perspective since the Swampland Conjecture on Trans-Planckian Censorship is automatically satisfied. We provide new analytic estimates for the bounce action and the tunneling rate in periodic potentials which replace the thin-wall approximation in the regime of fast tunneling. Finally, we study model implications and derive an upper limit of $\sim 10^{10}$ GeV on the axion decay constant in viable chain inflation with axions.