Modified Starobinsky inflation by the $R\ln \left(\square \right)R$ term

Abstract

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.

arXiv comment22 pages, 3 figures; v3: matches the published version

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