Modified Starobinsky inflation by the $R\ln\left( \square\right) R$ 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: $R^{2}$, $C_{\kappa\rho\alpha\beta}C^{\kappa\rho\alpha\beta}$,
$R\ln\left( \square\right) R$ and $C_{\kappa\rho\alpha\beta}\ln\left(
\square\right) C^{\kappa\rho\alpha\beta}$. 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
$R\ln\left( \square\right) R$, 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.
