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

TL;DR

This work develops a rescaled $\mathcal{R}^2$-corrected minimally coupled scalar field theory in the Jordan frame, yielding a perturbative, single-field description with a potentially stronger primordial gravity via a rescaled constant $G/\lambda$. It derives analytic slow-roll indices and observables for a general $f(\mathcal{R},\phi)$ framework and applies the formalism to three canonical potentials (hybrid, monomial, power-law). The results show that two strong-gravity models (hybrid and power-law) can be made compatible with ACT data, while the weak-gravity monomial model, although ACT-compatible in parameter choices, suffers a breakdown of the perturbative expansion. The findings demonstrate that curvature corrections in the Jordan frame can revive single-field inflation as compatible with ACT/Planck constraints, and suggest future work including extensions to Einstein–Gauss–Bonnet terms.

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 $\sim λ\frac{\mathcal{R}}{16πG}$, the gravitational constant will no longer be that of Newton's, but a rescaled one $\frac{G}λ$ 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.

Figures (6)

• Figure 1: The 2018 marginalized Planck likelihood curves, the ACT constraints and the updated Planck constraints on the tensor-to-scalar ratio, versus the rescaled $\mathcal{R}^2$-corrected hybrid inflation model for $\mathcal{V}_0=8\times 10^{-12}$, $\beta=0.000004$, $\lambda=0.1$, and $N$ in the range $N=[50,60]$.
• Figure 2: The behavior of the slow-roll indices $\epsilon_1$, $\epsilon_2$, $\epsilon_3$ and $\epsilon_4$, for the rescaled hybrid inflation model in the $e$-foldings range $N=[0,60]$. We used the values of the free parameters $\mathcal{V}_0=8\times 10^{-12}$, $\beta=0.000004$, $\lambda=0.1$ and for $N$ in the range $N=[0,60]$.
• Figure 3: The 2018 marginalized Planck likelihood curves, the ACT constraints and the updated Planck constraints on the tensor-to-scalar ratio, versus the rescaled $\mathcal{R}^2$-corrected monomial inflation model for $\mathcal{V}_0=0.000000001$, $\beta=0.000001$, $\lambda=16.11$, and $\delta=-0.45$, and $N$ in the range $N=[50,60]$.
• Figure 4: The behavior of the slow-roll indices $\epsilon_1$, $\epsilon_2$, $\epsilon_3$ and $\epsilon_4$, for the rescaled monomial inflation model in the $e$-foldings range $N=[0,60]$. We used the values of the free parameters $\mathcal{V}_0=0.000000001$, $\beta=0.000001$ and $\lambda=16.11$, and $\delta=-0.45$ and for $N$ in the range $N=[0,60]$.
• Figure 5: The 2018 marginalized Planck likelihood curves, the ACT constraints and the updated Planck constraints on the tensor-to-scalar ratio, versus the rescaled $\mathcal{R}^2$-corrected power-law inflation model for $\mathcal{V}_0=8\times 10^{-12}$, $\beta=0.000004$, $\lambda=0.1$, and $N$ in the range $N=[50,60]$.