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

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