Robustness of predicted CMB fluctuations in Cartan F(R) gravity

We investigated the cosmology of F ( R ) gravity rebuilt with the Cartan formalism. This is called Cartan F ( R ) gravity. The well-known F ( R ) gravity has been introduced to extend the standard cosmology, e.g., to explain the cosmological accelerated expansion as inflation. Cartan F ( R ) gravity is based on the Riemann-Cartan geometry. The curvature R is separated into two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming a matter-independent spin connection, 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. This feature simplifies the building and analysis of a new model of inflation. In this paper, we study two models, the power-law model, and the logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found robust CMB fluctuations via analytical computation and confirmed this feature through numerical calculations.