Aspects of nonlinear perturbations in cosmological models

Abstract

Nonlinearities in the perturbations of the cosmological models may be important. This paper briefly reviews three cases in which we have studied the effects of such nonlinearities. In de Sitter spacetime, the bare necessity that the perturbations should be a part of a consistent expansion of the field equations leads to the requirement, using the so-called linearization stability arguments developed in the 1970s, that the quantum field theory of a scalar field on de Sitter spacetime should de Sitter invariant—not covariant. In other words, all states of the field should be de Sitter invariant. For the Einstein static universe these constraints lead to the conclusion that all pertubations are unstable. This follows from the requirement that all perturbations must include the homogeneous mode at equal amplitude to the other modes if the linearization stabilty constraints are to be satisfied. Finally, the concern that the effect of second-order perturbations on the long-wavelength (super-Hubble modes) perturbations could be much stronger than that of the first-order perturbations for a large range of slow-roll conditions was explored. While this result is gauge dependent, and is the result of a variety of poorly controlled approximations (in particular, in the handling of the ultraviolet divergences) it is worrying in its implications for the conclusions drawn from the various inflationary scenarios.