Predictions from an anisotropic inflationary era

Abstract

This paper investigates the predictions of an inflationary phasestarting from a homogeneous and anisotropic universe of theBianchi I type. After discussing the evolution of the background spacetime, focusing on the number ofe-folds and the isotropization, we solve the perturbation equations and predict the powerspectra of the curvature perturbations and gravity waves at the end of inflation.The main features of the early anisotropic phase is (1) a dependence of the spectra onthe direction of the modes, (2) a coupling between curvature perturbations andgravity waves and (3) the fact that the two gravity wave polarizations do not sharethe same spectrum on large scales. All these effects are significant only on largescales and die out on small scales where isotropy is recovered. They depend on acharacteristic scale that can, but a priori must not, be tuned to some observable scale.To fix the initial conditions, we propose a procedure that generalizes the one standardlyused in inflation but that takes into account the fact that the WKB regime is violated atearly times when the shear dominates. We stress that there exist modes that do not satisfythe WKB condition during the shear-dominated regime and for which the amplitude at theend of inflation depends on unknown initial conditions. On such scales, inflation loses itspredictability.This study paves the way for the determination of the cosmological signature of a primordial shear, whateverthe Bianchi I spacetime. It thus stresses the importance of the WKB regime to drawinflationary predictions and demonstrates that, when the number ofe-folds is large enough, the predictions converge toward those of inflation in a Friedmann–Lemaîtrespacetime but that they are less robust in the case of an inflationary era with a small number ofe-folds.