Strong Gravity Effects on $\mathcal{R}^2$-corrected Single Scalar Field Inflation and Compatibility with the ACT Data

TL;DR

This paper introduces a rescaled $ ^2$-corrected scalar field inflation model incorporating quantum corrections, analyzing its implications for early universe gravity strength and compatibility with ACT observational data.

Contribution

It develops a novel theoretical framework for $ ^2$-corrected scalar inflation with quantum corrections, allowing for variable primordial gravity strength and analytical tractability.

Findings

The model predicts a rescaled gravitational constant affecting inflation dynamics.

Quantum corrections modify inflationary potentials and their observational signatures.

Compatibility with ACT data supports the viability of the proposed framework.

Abstract

In this work we introduce the rescaled $\mathcal{R}^2$-corrected minimally coupled scalar field theory, a theory that contains minimal quantum corrections of the single scalar field Lagrangian. We develop the theoretical framework in the string frame where the baryons geodesics are free fall geodesics and we do not treat the theory as a two scalar field theory in the Einstein frame. The theoretical framework can be reduced to a single scalar field theory framework by using a perturbative expansion at the level of the field equations, making the resulting theory easy to tackle analytically. The first two quantum corrections contain two terms, a linear $\sim \mathcal{R}$ and a quadratic term $\sim \mathcal{R}^2$. The effect of the linear term alters the Einstein-Hilbert term, making the resulting theory a rescaled version of Einstein-Hilbert gravity. Due to the presence of the rescaled Einstein-Hilbert term $\sim \lambda \frac{\mathcal{R}}{16\pi G}$, the gravitational constant will no longer be that of Newton's, but a rescaled one $\frac{G}{\lambda}$ and hence gravity can be stronger primordially, or even weaker. The perspective of having stronger gravity primordially, is compatible with intuition, since one expects a stronger gravity primordially, but having a weaker gravity for some reason is not prohibited theoretically. The attribute of our theoretical framework is that it allows a stronger gravity primordially, which returns to ordinary gravity as the curvature of the Universe decreases. We examine the effects of the quantum terms on several mainstream scalar field inflationary potentials, such as hybrid inflation, monomial inflation and power-law inflation.