Long-Wavelength Modes of Cosmological Scalar Fields

Scalar fields have played a major role in attempts to model the early Universe. In particular, nearly every incarnation of the inflation scenario has relied on scalars to generate vacuum energy and in turn exponential expansion and density fluctuations. Many of these models rely on slow roll potentials, i.e., potentials that are nearly flat where the scalar masses can be very small. Recently, horizon size and super horizon size density perturbations have been studied intensively, because of their importance for understanding low l modes (see [1] and references therein) in the WMAP data [2]. Long wavelength scalar field modes have interesting properties when the wavelength is on the order of the horizon size cH−1 0 . One finds dispersion and diffraction effects that depend on the scalar mass and it’s coupling to gravity. The generic lagrangian for a scalar in a Friedmann-Robertson-Walker (FRW) Universe is