Quantization of Perturbations in an Inflating Elastic Solid

Abstract

A sufficiently rigid relativistic elastic solid can be stable for negative pressure values and thus is capable of driving a stage of accelerated expansion. If a relativistic elastic solid drove an inflationary stage in the early Universe, quantum mechanically excited perturbations would arise in the medium. We quantize the linear scalar and tensor perturbations and investigate the observational consequences of having such an inflationary period. We find that slowly varying sound speeds of the perturbations and a slowing varying equation of state of the solid can produce a slightly red-tilted scalar power spectrum that agrees with current observational data. Even in the absence of nonadiabatic pressures, perturbations evolve on superhorizon scales, due to the shear stresses within the solid. As such, the spectra of perturbations are in general sensitive to the details of the end of inflation and we characterize this dependence. Interestingly, we uncover here accelerating solutions for elastic solids with (1 + P/ρ) significantly greater than 0 that nevertheless have nearly scale-invariant scalar and tensor spectra. Beyond theoretical interest, this may allow for the possibility of viable inflationary phenomenology relatively far from the de Sitter regime.