ANALYTIC SOLUTION FOR MATTER DENSITY PERTURBATIONS IN A CLASS OF VIABLE COSMOLOGICAL f(R) MODELS

For a class of viable cosmological models in f(R) gravity in which deviation from the Einstein gravity decreases as an inverse power law of the Ricci scalar R for large R, an analytic solution for density perturbations in the matter component during the matter-dominated stage is obtained in terms of hypergeometric functions. An analytical expression for the matter transfer function at scales much smaller than the present Hubble scale is also obtained.