Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation

Abstract

We study inflation with the most general non-degenerate gravitational action that depends on the symmetric part of the Ricci tensor coupled to a scalar field in the Palatini formulation of gravity. We use field redefinitions to shift the effect of the Ricci terms from gravity to the scalar field, and apply the result to slow-roll inflation. As examples, we consider actions quadratic and cubic in the Ricci tensor. In the quadratic case the results are similar to the case $R+\alpha R^2$ that has been studied earlier: the tensor-to-scalar ratio $r$ can be suppressed by an arbitrary amount, while the scalar spectrum is unaffected. In the cubic case, $r$ can be suppressed by at most a factor of $2/9$, and the change in the scalar spectral index $n_s$ can be large.

arXiv comment12+4 pages, 2 figures. v2: added references, clarified text. v3: added a reference, clarified text. Published version

References in corpus (50)

• Planck 2018 results. X. Constraints on inflation
• The Standard Model Higgs boson as the inflaton
• Healthy theories beyond Horndeski
• Higgs inflation: consistency and generalisations
• Horndeski theory and beyond: a review
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• Avoiding Dark Energy with 1/R Modifications of Gravity
• On the Naturalness of Higgs Inflation
• Power-counting and the Validity of the Classical Approximation During Inflation
• Comment on Higgs Inflation and Naturalness
• On Inflation with Non-minimal Coupling
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Question of quantum equivalence between Jordan frame and Einstein frame
• Higgs-Palatini Inflation and Unitarity
• Higgs Inflation and Naturalness
• Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
• Ghosts in metric-affine higher order curvature gravity
• Inflation with $R^2$ term in the Palatini formalism
• Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton inflations
• A Unitarity-Conserving Higgs Inflation Model
• Self-healing of unitarity in Higgs inflation
• Cosmological disformal invariance
• Quantum Effects in Palatini Higgs Inflation
• Higgs Gravitational Interaction, Weak Boson Scattering, and Higgs Inflation in Jordan and Einstein Frames
• Conformal invariance of curvature perturbation
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Disformal transformation of cosmological perturbations
• Late and early time phenomenology of Higgs-dependent cutoff
• General invertible transformation and physical degrees of freedom
• The Ostrogradsky instability can be overcome by quantum physics
• Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory
• Gravitational Interaction of Higgs Boson and Weak Boson Scattering
• Curvature perturbation in multi-field inflation with non-minimal coupling
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Unitarity-violation in Generalized Higgs Inflation Models
• Dynamical Emergence of Scalaron in Higgs Inflation
• Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
• Beyond dimensional analysis: Higgs and new Higgs inflations {\it do not} violate unitarity
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Disformal invariance of curvature perturbation
• Critical point Higgs inflation in the Palatini formulation
• Cosmological Perturbations in Palatini Formalism
• Unitarity and predictiveness in new Higgs inflation
• Does Palatini Higgs Inflation Conserve Unitarity?
• Uniqueness of the gauge invariant action for cosmological perturbations
• Multi-disformal invariance of nonlinear primordial perturbations
• On Preheating in Higgs Inflation
• Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity
• Disformal invariance of cosmological observables

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• Palatini $R^2$ Quintessential Inflation
• Implications of Palatini gravity for inflation and beyond
• Slow-roll inflation in Palatini $F(R)$ gravity
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Preheating in Einstein-Cartan Higgs Inflation: Oscillon formation
• On the number of $e$-folds in the Jordan and Einstein frames
• Multiple point criticality principle and Coleman-Weinberg inflation
• Stability of non-degenerate Ricci-type Palatini theories
• Observable Gravitational Waves from Hyperkination in Palatini Gravity and Beyond
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Beyond (and back to) Palatini quadratic gravity and inflation
• $\tilde{\xi }$-attractors in metric-affine gravity
• Isocurvature modes and non-Gaussianity in affine inflation
• Natural inflation in Palatini $F(R,X)$
• Ephemeral Oscillons in Scalar-Tensor Theories: The Higgs-like case
• Cosmic inflation in metric-affine gravity
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity