Speaker
Description
In this work we analyze the stability criteria in $f(R)$ theories of gravity in the metric formalism under the approach of a thermodynamics analogy proposed in [C.D. Peralta and S.E. Jorás JCAP06(2020)053] for $\phi^4$ and double well inflationary potentials. We starting from the mentioned potentials in the Einstein frame, and obtain a parametric form of $f(R)$ in the corresponding Jordan frame. Such approach yields plenty of new pieces of information, namely a self-terminating inflationary solution with a linear Lagrangian, a robust criterion for stability of such theories, and a dynamical effective potential for the Ricci scalar $R$.
The addition of an ad-hoc Cosmological Constant in the Einstein frame leads to a Thermodynamical interpretation of this physical system described by a Van der Waals like behavior, which allows whole thermodynamics picture then follows: a equation of state, binodal and spinodal curves, phase transition, critical quantities (pressure, volume and temperature), entropy jumps, specific-heat divergence (and the corresponding critical exponent).
