  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/\rho) 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.
