$\mathcal{R}^2$ Quantum Corrected Scalar Field Inflation

TL;DR

This paper investigates how quantum corrections of the $ ^2$ type influence scalar field inflation, demonstrating that such corrections can produce viable inflationary models, exemplified through a quantum-corrected quadratic inflation scenario.

Contribution

It introduces a quantum-corrected scalar field inflation model with $ ^2$ corrections in the string frame, analyzing its inflationary dynamics and viability, which is a novel approach compared to previous Einstein frame studies.

Findings

Quantum corrections modify slow-roll parameters.

The $ ^2$ quantum corrected model yields viable inflationary predictions.

Compared to simple quadratic inflation, the corrected model aligns better with observations.

Abstract

String theory enjoys an elevated role among quantum gravity theories, since it seems to be the most consistent UV completion of general relativity and the Standard Model. However, it is hard to verify the existence of this underlying theory on terrestrial accelerators. One way to probe string theory is to study its imprints on the low-energy effective inflationary Lagrangian, which are quantified in terms of high energy correction terms. It is highly likely, thus, to find higher order curvature terms combined with string moduli, that is scalar fields, since both these types of interactions and matter fields appear in string theory. In this work we aim to stress the probability that the inflationary dynamics are controlled by the synergy of scalar fields and higher order curvature terms. Specifically, we shall consider a well motivated quantum corrected canonical scalar field theory, with the quantum corrections being of the $\mathcal{R}^2$ type. The reason for choosing minimally coupled scalar theory is basically because if scalar fields are evaluated in their vacuum configuration, they will either be minimally coupled or conformally coupled. Here we choose the former case, and the whole study shall be performed in the string frame (Jordan frame), in contrast to similar studies in the literature where the Einstein frame two scalar theory is considered. We derive the field equations of the quantum-corrected theory at leading order and we present the form the slow-roll indices obtain for the quantum corrected theory. We exemplify our theoretical framework by using the quadratic inflation model, and as we show, the $\mathcal{R}^2$ quantum corrected quadratic inflation model produces a viable inflationary phenomenology, in contrast with the simple quadratic inflation model.