The thermal view of $f(R)$ cosmology

A new thermal view of scalar-tensor gravity, in which general relativity is the zero-temperature state of gravity, is applied to the specific subclass of $f(R)$ gravity theories and, specifically, to spatially homogeneous and isotropic universes. Within the limits of application of the new thermal formalism, results on the convergence to Einstein cosmology (or lack thereof) are first obtained for general $f(R)$ theories, and then illustrated with power-law and Starobinsky $f(R)$ gravity.