Generalized $R^p$-attractor Cosmology in the Jordan and Einstein Frames: New Type of Attractors and Revisiting Standard Jordan Frame $R^p$ Inflation

Abstract

In this work we shall study a new class of attractor models which we shall call generalized $R^p$-attractor models. This class of models is based on a generalization of the Einstein frame potential of $R^p$ $f(R)$ gravity models in the Jordan frame. We present the attractor properties of the corresponding non-minimally coupled Jordan frame theory, and we calculate the observational indices of inflation in the Einstein frame. As we show, there is a large class of non-minimally coupled scalar theories, with an arbitrary non-minimal coupling which satisfies certain conditions, that yield the same Einstein frame potential, this is why these models are characterized attractors. As we demonstrate, the generalized $R^p$-attractor models are viable and well fitted within the Planck constraints. This includes the subclass of the generalized $R^p$-attractor models, namely the Einstein frame potential of $R^p$ inflation in the Jordan frame, a feature also known in the literature. We also highlight an important issue related to the $R^p$ inflation in the Jordan frame, which is known to be non-viable. By conformal invariance, the $R^p$ inflation model should also be viable in the Jordan frame, which is not. We pinpoint the source of the problem using two different approaches in the $f(R)$ gravity Jordan frame, and as we demonstrate, the problem arises in the literature due to some standard simplifications made for the sake of analyticity. We demonstrate the correct way to analyze $R^p$ inflation in the Jordan frame, using solely the slow-roll conditions.

IJMPD Accepted

References in corpus (22)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Standard Model Higgs boson as the inflaton
• Inflationary Cosmology
• Large Field Inflation and Double $\alpha$-Attractors
• Causal Limit of Neutron Star Maximum Mass in $f(R)$ Gravity in View of GW190814
• Slowly rotating neutron and strange stars in $R^2$ gravity
• Sensitivity to a Frequency-Dependent Circular Polarization in an Isotropic Stochastic Gravitational Wave Background
• Single-field $\alpha$-attractors
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Perturbation, Non-Gaussianity and Reheating in a GB-$\alpha$-Attractor Model
• Cosmological Attractor Models and Higher Curvature Supergravity
• Inflationary $\alpha$-attractors from $F(R)$ Gravity
• Consistency relation for $R^p$ inflation
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Inflationary Attractors in $F(R)$ Gravity
• On the maximum mass limit of neutron stars in scalar-tensor gravity
• Reconstructing a $f(R)$ theory from the $\alpha$-Attractors
• Nonminimal coupling and inflationary attractors
• Universal Inflationary Attractors Implications on Static Neutron Stars
• Inflation beyond T-models and primordial B-modes
• $\alpha$-attractor dark energy in view of next-generation cosmological surveys
• Bouncing Cosmologies

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• Power law $\alpha$-Starobinsky inflation
• Complementary signatures of $\alpha -$attractor inflation in CMB and cosmic string Gravitational Waves