Viable mimetic F(R) gravity compatible with Planck observations

Using the mimetic matter approach, we study F(R) gravity with scalar potential and Lagrange multiplier constraint. As we demonstrate, for a given F(R) gravity and for suitably chosen mimetic potential, it is possible to realize inflationary cosmology consistent with Planck observations. We also investigate the de Sitter solutions of the mimetic F(R) theory and study the stability of the solutions, when these exist, towards linear perturbations, with the unstable solutions, which can provide a mechanism for graceful exit from inflation. Finally, we describe a reconstruction method which can yield the F(R) gravity that can generate realistic inflationary cosmological evolution, given the mimetic potential and the Hubble rate.