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This article investigates the predictions of an inflationary phase startingfrom a homogeneous and anisotropic universe of the Bianchi I type. Afterdiscussing the evolution of the background spacetime, focusing on the number ofe-folds and the isotropization, we solve the perturbation equations and predictthe power spectra of the curvature perturbations and gravity waves at the endof inflation. The main features of the early anisotropic phase is (1) adependence of the spectra on the direction of the modes, (2) a coupling betweencurvature perturbations and gravity waves, and (3) the fact that the twogravity waves polarisations do not share the same spectrum on large scales. Allthese effects are significant only on large scales and die out on small scaleswhere isotropy is recovered. They depend on a characteristic scale that can,but a priori must not, be tuned to some observable scale. To fix the initialconditions, we propose a procedure that generalises the one standardly used ininflation but that takes into account the fact that the WKB regime is violatedat early times when the shear dominates. We stress that there exist modes thatdo not satisfy the WKB condition during the shear-dominated regime and forwhich the amplitude at the end of inflation depends on unknown initialconditions. On such scales, inflation loses its predictability. This studypaves the way to the determination of the cosmological signature of aprimordial shear, whatever the Bianchi I spacetime. It thus stresses theimportance of the WKB regime to draw inflationary predictions and demonstratesthat when the number of e-folds is large enough, the predictions convergetoward those of inflation in a Friedmann-Lemaitre spacetime but that they areless robust in the case of an inflationary era with a small number of e-folds.

Predictions from an anisotropic inflationary era