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

The cosmology of the $F(R)$ gravity rebuilding by the Cartan formalism is investigated. 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 the inflation. Cartan $F(R)$ gravity is based on the Riemann-Cartan geometry. The curvature $R$ can separate to two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming the 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 building and analysis of new model of inflation. In this paper, we study two models, the power-law model and logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found the robustness of CMB fluctuation by the analytical computation and confirm this feature by the numerical calculation.