Cosmological perturbations in coherent oscillating scalar field models

Abstract

Abstract: The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V(ϕ) = λ|ϕ|n/n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained ceff2 = ω = (n − 2)/(n + 2) with ω the effective equation of state. We also obtain the first order correction in k2/ωeff2, when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ωeff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet’s theorem.