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

TL;DR

This paper investigates how the nonlocal term $R ext{ln}(oxempty) R$ modifies Starobinsky inflation, showing it behaves like a local model with a canonical scalar field and constrains parameters using CMB data.

Contribution

It introduces and analyzes the effects of the $R ext{ln}(oxempty) R$ nonlocal term on Starobinsky inflation, demonstrating its equivalence to a local scalar field model.

Findings

The nonlocal term acts as a small correction to the $R^2$ inflation model.

The model can be approximated by a local scalar field theory in the Einstein frame.

Constraints on model parameters are obtained from CMB observations.

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.