Cosmological perturbations in the presence of a solid with positive pressure

Abstract

Evolution of scalar perturbations in a universe containing solid matter with positive pressure is studied. Solution for pure solid is found and matched with solution for ideal fluid, including the case when the pressure to energy density ratio $w$ has a jump. Two classes of solutions are explored in detail, solutions with radiation-like solid ($w = 1/3$) and solutions with stiff solid ($w > 1/3$) appearing in a universe filled with radiation. For radiation-like solid, an almost flat spectrum of large-scale perturbations is obtained only if the shear stress to energy density ratio $\xi$ is close to zero, $|\xi| \lesssim 10^{-5}$. For a solid with stiff equation of state, large-scale perturbations are enhanced for $\xi$ negative and suppressed for $\xi$ positive. If the solid dominated the dynamics of the universe long enough, perturbations could end up suppressed as much as by several orders of magnitude, and in order that the inclination of the large-scale spectrum is consistent with observations, radiation must have prevailed over the solid long enough before recombination. In Newtonian gauge, corrections to metric and energy density are typically much greater than 1 in the first period after the shear stress appears, but the linearized theory is still applicable because the corrections stay small when one uses the proper-time comoving gauge.