Spatial Curvature Falsifies Eternal Inflation
Matthew Kleban, Marjorie Schillo

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…
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