Modified Starobinsky inflation by the R ln (□) R term

In the context of effective theories of gravity, a minimalist bottom-up approach which takes into account 1-loop quantum corrections leads to modifications in the Einstein-Hilbert action through the inclusion of four extra terms: R-2, C kappa rho alpha beta C kappa rho alpha beta, R ln (square) R and C-kappa rho alpha beta ln (square) C-kappa rho alpha beta. The first two terms are necessary to guarantee the renormalizability of the gravitational theory, and the last two terms (nonlocal terms) arise from the integration of massless/light matter fields. This work aims to analyze how one of the nonlocal terms, namely R ln (square) R, affects the Starobinsky inflation. We consider the nonlocal term as a small correction to the R-2 term, and we demonstrate that the model behaves like a local model in this context. In addition, we show that the approximate model in the Einstein frame is described by a canonical scalar field minimally coupled to general relativity. Finally, we study the inflationary regime of this model and constrain its free parameters through observations of CMB anisotropies.