Scale invariant curvature perturbations from a spontaneously decaying scalar field

Abstract

The evolution of superhorizon curvature perturbations in a two-component interacting universe is considered. It is found that adiabatic modes conserve the total curvature perturbation $\zeta$, unless there are stages in which the rate of dissipation of one component into another is not constant. Moreover, our result shows that when the rate is varying it is possible for 'isocurvature' perturbations generated during reheating to alter the amplitude of an adiabatic curvature mode even when the mode is outside the horizon. Specifically, if an indefinitely large rate $\Gamma$ for massive particles decaying into photons develops rapidly amid vanishingly small initial values (before decay) of the total curvature $\zeta_i$ and Newtonian potential $\Phi_i$, such that the product $\Gamma\zeta_i$ and $\Gamma\Phi_i$ become a pair of finite and universal constants for all superhorizon scales afterwards, Harrison-Zel'dovich scale-invariant power spectrum could be synthesized from a homogeneous state without inflation at all.