Signatures of the very early Universe: Inflation, spatial curvature, and large scale anomalies

Abstract

A short inflationary phase may not erase all traces of the primordial Universe. Associated observables include both spatial curvature and "anomalies" in the microwave background or large-scale structure. The present curvature Ω_{K ,0} reflects the initial curvature, Ω_{K ,start} , and the angular size of anomalies depends on k_start, the comoving horizon size at the onset of inflation. We estimate posteriors for Ω_{K ,start} and k_start using current data and simulations, and show that if either quantity is measured to have a nonzero value, both are likely to be observable. Mappings from Ω_{K ,start} and k_start to present-day observables depend strongly on the primordial equation of state; Ω_{K ,0} spans 10 orders of magnitude for a given Ω_{K ,start}, while a simple and general relationship connects Ω_{K ,0} and k_start. We show that current bounds on Ω_{K ,0} imply that if k_start is measurable, the curvature was already small when inflation began. Finally, since the energy density changes slowly during inflation, primordial gravitational wave constraints require that a short inflationary phase be preceded by a nontrivial preinflationary phase with critical implications for the expected value of Ω_{K ,start}.