Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity

We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f(R) and f(R,RμνR μν) theories of gravity and consider the existence of non-singular bouncing solutions in the early universe. We find that all f(R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R+ aR/RP +RμνR /RP exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a < 0) and radiation (for arbitrary a). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic (w > 1) sources of matter/energy.