Statistical anisotropy in the inflationary universe

Abstract

During cosmological inflation, quasiclassical perturbations are permanently generated on super-Hubble spatial scales, their power spectrum being determined by the fundamental principles of quantum field theory. By the end of inflation, they serve as primeval seeds for structure formation in the universe. At early stages of inflation, such perturbations break homogeneity and isotropy of the inflationary background. In the present paper, we perturbatively take into account this quasiclassical background inhomogeneity of the inflationary universe while considering the evolution of small-scale (sub-Hubble) quantum modes. As a result, the power spectrum of primordial perturbations develops statistical anisotropy, which can subsequently manifest itself in the large-scale structure and cosmic microwave background. The statistically anisotropic contribution to the primordial power spectrum is predicted to have almost scale-invariant form dominated by a quadrupole. Theoretical expectation of the magnitude of this anisotropy depends on the assumptions about the physics in the trans-Planckian region of wave numbers.