Inflation in $F(R)$ gravity models revisited after ACT

Abstract

The $F(R)$ gravity models of inflation are revisited in light of the recent observations of cosmic microwave background radiation by Atacama Cosmology Telescope (ACT) and DESI Collaboration. A detailed study of the evolution equations in the Jordan frame is given and a new description of the slow-roll approximation in the $F(R)$-gravity-based models of inflation is proposed. It is found that all those models of inflation are significantly constrained by demanding a higher (than the Planck Telescope value) cosmological tilt $n_s$ of scalar perturbations and a positive running index ${\alpha }_s$ favored by ACT. It is not difficult to meet the ACT constraints on the scalar tilt $n_s$ by modifying the existing models of inflation, but simultaneously demanding a positive running ${\alpha }_s$ would rule out many of them. Using the proposed slow-roll approximation in the Jordan frame, we provide a new modification of the Starobinsky inflation model in the framework of $F(R)$ gravity, which satisfies all ACT constraints. An extension of our ACT-consistent inflation model to the unified $F(R)$-gravity description of Starobinsky-like inflation and production of primordial black holes on a smaller scale is also proposed.

21 pages in JCAP format, Section 9 and references added, Sections 1 and 10 revised

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Cited by in corpus (7)

• Harrison-Zeldovich attractor: From Planck to ACT results
• Primordial black holes formation in inflationary $F(R)$ models with scalar fields
• Reheating in geometric Weyl-invariant Einstein-Cartan gravity
• Effect of $R^2$ on the stability of de Sitter solution of the generalized Einsteinian cubic gravity
• Reconciling the ACT Preference in $f(T)$ Gravity: Inflation and Reheating Constraints
• Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models
• Constraints on non-canonical chaotic inflation from ACT DR6 and BICEP/Keck data