EVOLUTION OF SCALAR FIELD COSMOLOGICAL PERTURBATIONS

A method of dealing with cosmological perturbations was suggested recently which allows a simple way of choosing the gauge appropriate to each separate problem. Using this method, if we have one solution in a particular gauge we can easily derive the rest of the solutions in all the other gauges. In this paper we apply the method to a medium dominated by a minimally coupled scalar field. By considering full metric perturbations we are doing scalar field quantum field theory in a spatially flat homogeneous and isotropic background spacetime, now including the metric perturbations as additional quantum fields consistently excited from the scalar field perturbations. Asymptotic solutions in a general potential case, and the exact solutions in an exponential potential case-thus a power-law expanding background case-are presented in tabular forms. Perturbations in de Sitter space-thus an exact exponentially expanding background case-need a separate treatment which is also presented. It is interesting to note that it is in the case that takes into account the full metric perturbations which allows more self-consistent analysis, compared to the one based on pure background metric. We identify the uniform-curvature gauge as providing the simple analysis in the scalar field perturbations. The full solutions may provide a wider perspective on the subject.