Study of General Relativity and f(R) Modified Gravity with Cosmological Constant for Einstein and Jordan Frames
Abstract
This thesis investigates a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian f(R) in the Jordan frame -- we start from a simple φ2 potential in the Einstein frame and investigate the corresponding f(R) in the former picture. 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, 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, which allows further insight on its (meta)stability and evolution.