First-order thermodynamics of scalar-tensor cosmology

A new thermodynamics of scalar-tensor gravity is applied to spatially homogeneous and isotropic cosmologies in this class of theories and tested on analytical solutions. A forever-expanding universe approaches the Einstein "state of equilibrium" with zero effective temperature at late times and departs from it near spacetime singularities. "Cooling" by expansion and "heating" by singularities compete near the Big Rip, where it is found that the effective temperature diverges in the case of a conformally coupled scalar field.