Spatial Curvature Falsifies Eternal Inflation

TL;DR

The paper argues that precise measurements of spatial curvature _k can decisively test and potentially falsify different models of eternal inflation, with upcoming experiments playing a crucial role.

Contribution

It establishes a direct link between CMB multipole moments and the falsifiability of eternal inflation models based on spatial curvature measurements.

Findings

|_k| > 10^-4 rules out slow-roll eternal inflation

_k < -10^-4 rules out false-vacuum eternal inflation

Future experiments will significantly improve _k measurement sensitivity

Abstract

Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are O(10^-5). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature \Omega_k. On this basis we argue that a measurement of |\Omega_k| > 10^-4 would rule out slow-roll eternal inflation in our past with high confidence, while a measurement of \Omega_k < -10^-4 (which is positive curvature, a locally closed universe) rules out false-vacuum eternal inflation as well, at the same confidence level. In other words, negative curvature (a locally open universe) is consistent with false-vacuum eternal inflation but not with slow-roll eternal inflation, and positive curvature falsifies both. Near-future experiments will dramatically extend the sensitivity of \Omega_k measurements and constitute a sharp test of these predictions.