Cartan F(R) Gravity and Equivalent Scalar–Tensor Theory

Abstract

We investigate the Cartan formalism in F(R) gravity. F(R) gravity has been introduced as a theory to explain cosmologically accelerated expansions by replacing the Ricci scalar R in the Einstein–Hilbert action with a function of R. As is well-known, F(R) gravity is rewritten as a scalar–tensor theory by using the conformal transformation. Cartan F(R) gravity is described based on the Riemann–Cartan geometry formulated by the vierbein-associated local Lorenz symmetry. In the Cartan formalism, the Ricci scalar R is divided into two parts: one derived from the Levi–Civita connection and the other from the torsion. Assuming the spin connection-independent matter action, we have successfully rewritten the action of Cartan F(R) gravity into the Einstein–Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. red Thus, symmetries in Cartan F(R) gravity are clearly conserved. The resulting scalar–tensor theory is useful in applications of the usual slow-roll scenario. As a simple case, we employ the Starobinsky model and evaluate fluctuations in cosmological microwave background radiation.