Inflation with $R^2$ term in the Palatini formalism

Abstract

We study scalar field inflation in $F(R)$ gravity in the Palatini formulation of general relativity. Unlike in the metric formulation, in the Palatini formulation $F(R)$ gravity does not introduce new degrees of freedom. However, it changes the relations between existing degrees of freedom, including the inflaton and spacetime curvature. Considering the case $F(R)=R+\alpha R^2$, we find that the $R^2$ term decreases the height of the effective inflaton potential. By adjusting the value of $\alpha$, this mechanism can be used to suppress the tensor-to-scalar ratio $r$ without limit in any scalar field model of inflation without affecting the spectrum of scalar perturbations.

9 pages, no figures. v2. Added references and clarifications. Published version

References in corpus (34)

• f(R) Theories Of Gravity
• The Standard Model Higgs boson as the inflaton
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Metric-affine f(R) theories of gravity
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Palatini form of 1/R gravity
• Cosmological perturbations in the Palatini formulation of modified gravity
• Higher order gravity theories and scalar tensor theories
• Nonmetricity formulation of general relativity and its scalar-tensor extension
• Higgs-Palatini Inflation and Unitarity
• Higgs Scalaron Mixed Inflation
• Classical and Quantum Initial Conditions for Higgs Inflation
• Higgs inflation with loop corrections in the Palatini formulation
• Inflation in the Mixed Higgs-$R^2$ Model
• Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton inflations
• The spectrum of symmetric teleparallel gravity
• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Higgs Starobinsky Inflation
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Mapping Ricci-based theories of gravity into general relativity
• The Palatini side of inflationary attractors
• Palatini versus metric formulation in higher curvature gravity
• Resurrecting Quadratic Inflation with a non-minimal coupling to gravity
• Quantum corrections to quartic inflation with a non-minimal coupling: metric vs. Palatini
• Higgs inflation at the hilltop
• Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics
• Primordial perturbations generated by Higgs field and $R^2$ operator
• Attractor Behaviour in Multifield Inflation
• Microscopic and Macroscopic Behaviors of Palatini Modified Gravity Theories
• Initial Conditions for Critical Higgs Inflation
• Two-loop corrections to Starobinsky-Higgs inflation
• Variational and conformal structure of nonlinear metric-connection gravitational lagrangians
• Universality of the Einstein theory of gravitation

Cited by in corpus (93)

• The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe
• Anatomy of single-field inflationary models for primordial black holes
• Reheating in $R^2$ Palatini inflationary models
• Planck scale black hole dark matter from Higgs inflation
• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
• Dynamically induced Planck scale and inflation in the Palatini formulation
• Higgs inflation with the Holst and the Nieh-Yan term
• Higgs inflation in the Palatini formulation with kinetic terms for the metric
• Gauging scale symmetry and inflation: Weyl versus Palatini gravity
• Fractional attractors in light of the latest ACT observations
• Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
• Tracing the high energy theory of gravity: an introduction to Palatini inflation
• Palatini-Higgs inflation with non-minimal derivative coupling
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Junction conditions in Palatini $f(R)$ gravity
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Inflation in Metric-Affine Quadratic Gravity
• Dark matter from scalar field fluctuations
• Primordial backgrounds of relic gravitons
• Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?
• Trans-Planckian Censorship, Inflation and Dark Matter
• Palatini frames in scalar-tensor theories of gravity
• A simple $F(\mathcal{R},\varphi )$ deformation of Starobinsky inflationary model
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Axion dark matter from Higgs inflation with an intermediate $H_{\ast }$
• Tachyonic Preheating in Palatini $R^2$ Inflation
• Higgs inflation in metric and Palatini formalisms: Required suppression of higher dimensional operators
• Palatini $R^2$ Quintessential Inflation
• Towards distinguishing variants of non-minimal inflation
• Implications of Palatini gravity for inflation and beyond
• Higgs inflation and teleparallel gravity
• Gravitational dark matter production in Palatini preheating
• Sub-Planckian ${\varphi }^2$ Inflation in the Palatini Formulation of Gravity with an $R^2$ term
• Constant-roll in the Palatini-$R^2$ models
• Einstein-Cartan gravity, matter, and scale-invariant generalization
• Hillclimbing inflation in metric and Palatini formulations
• Critical point Higgs inflation in the Palatini formulation
• Initial conditions for plateau inflation: a case study
• Slow-roll inflation in Palatini $F(R)$ gravity
• Higgs-$R^2$ inflation -- full slow-roll study at tree-level
• Minimal $k$-inflation in light of the conformal metric-affine geometry
• Does Palatini Higgs Inflation Conserve Unitarity?
• Inflation and Reheating in f(R,h) theory formulated in the Palatini formalism
• New class of hybrid metric-Palatini scalar-tensor theories of gravity
• Non-minimal (self-)running inflation: metric vs. Palatini formulation
• Primordial black holes and induced gravitational waves from double-pole inflation
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Multiple point criticality principle and Coleman-Weinberg inflation
• Magnetogenesis in Higgs-Starobinsky inflation
• On the number of $e$-folds in the Jordan and Einstein frames
• Post-inflationary phases stiffer than radiation and Palatini formulation
• Bimetric-Affine Quadratic Gravity
• Ultraviolet behaviour of Higgs inflation models
• Tachyonic Preheating in Plateau Inflation
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• Inflation in Weyl-invariant Einstein-Cartan gravity
• Extended interactions in the Palatini-$R^2$ inflation
• Natural Inflation with non minimal coupling to gravity in $R^2$ gravity under the Palatini formalism
• Gravitational wave constraints on the observable inflation
• Testing scale-invariant inflation against cosmological data
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Observable Gravitational Waves from Hyperkination in Palatini Gravity and Beyond
• The Linear Regime of Tachyonic Preheating
• Einstein-Proca theory from the Einstein-Cartan formulation
• Invariant quantities of Scalar-Tensor Theories for stellar structure
• Cosmological constraints of Palatini $f(\mathcal{R})$ gravity
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Quintessential Inflation in Palatini Gravity
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• Palatini $F(R,X)$: a new framework for inflationary attractors
• Late time acceleration in Palatini gravity
• Beyond (and back to) Palatini quadratic gravity and inflation
• Dark Matter Production in Weyl $R^2$ Inflation
• Small free field inflation in higher curvature gravity
• General Einstein-Cartan quadratic gravity with derivative couplings
• $\tilde{\xi }$-attractors in metric-affine gravity
• Palatini formulation for gauge theory: implications for slow-roll inflation
• Note on initial conditions for small-field inflation
• General Analytical Conditions for Inflaton Fragmentation: Quick and Easy Tests for its Occurrence
• Palatini approach and large-scale magnetogenesis
• Quantum gravitational corrections to the inflationary power spectra in scalar-tensor theories
• Cosmic inflation from broken conformal symmetry
• Natural inflation in Palatini $F(R,X)$
• Toward a gravitational network: Bridging metric-affine gravity and no-scale supergravity
• Starobinsky Inflation with T-Model Kaehler Geometries
• On cosmological Inflation In Palatini $F(R,\varphi )$ Gravity
• Modelling Quintessential Inflation in Palatini Modified Gravity
• Natural inflation in Palatini $F(R)$
• Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models
• Large Field Polynomial Inflation in Palatini $f(R,\varphi )$ Gravity
• Cosmic inflation in metric-affine gravity
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity