Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature

Abstract

We consider ${\mathcal{R}}^2$-inflation in Palatini gravity, in the presence of scalar fields coupled to gravity. These theories, in the Einstein frame, and for one scalar field $h$, share common features with $K$ - inflation models. We apply this formalism for the study of single-field inflationary models, whose potentials are monomials, $V\sim h^n$, with $n$ a positive even integer. We also study the Higgs model non-minimally coupled to gravity. With ${\mathcal{R}}^2$-terms coupled to gravity as $\sim \alpha {\mathcal{R}}^2$, with $\alpha$ constant, the instantaneous reheating temperature $T_{ins}$, is bounded by $T_{ins}\le 0.290m_{Planck}/{\alpha }^{1/4}$, with the upper bound being saturated for large $\alpha$. For such large $\alpha$ need go beyond slow-roll to calculate reliably the cosmological parameters, among these the end of inflation through which $T_{ins}$ is determined. In fact, as inflaton rolls towards the end of inflation point, the quartic in the velocity terms, unavoidable in Palatini gravity, play a significant role and can not be ignored. The values of $\alpha$, and other parameters, are constrained by cosmological data, setting bounds on the inflationary scale $M_s\sim 1/\sqrt{\alpha }$ and the reheating temperature of the Universe.

35 pages, 18 figures, PDFLaTeX, text and references added, typos corrected

References in corpus (59)

• The Standard Model Higgs boson as the inflaton
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Higgs inflation: consistency and generalisations
• Reheating in Inflationary Cosmology: Theory and Applications
• Metric-affine f(R) theories of gravity
• Reheating constraints to inflationary models
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Reheating predictions in single field inflation
• Higgs inflation at the critical point
• Higgs inflation still alive
• Higgs-Palatini Inflation and Unitarity
• Higgs G-inflation
• Inflation and the Scale Dependent Spectral Index: Prospects and Strategies
• Higgs inflation from Standard Model criticality
• Higgs inflation with loop corrections in the Palatini formulation
• Preheating in Palatini Higgs inflation
• A Unitarity-Conserving Higgs Inflation Model
• Palatini versus metric formulation in higher curvature gravity
• Metric-affine Gravity and Inflation
• Minimal Higgs inflation with an $R^2$ term in Palatini gravity
• Resurrecting Quadratic Inflation with a non-minimal coupling to gravity
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Reheating temperature from the CMB
• Inflationary Perturbations in Palatini Generalised Gravity
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Quantum modes in DBI inflation: exact solutions and constraints from vacuum selection
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• K-inflationary Power Spectra in the Uniform Approximation
• Probing reheating with primordial spectrum
• $k$-essence $f(R)$ Gravity Inflation
• Inflationary dynamics and preheating of the non-minimally coupled inflaton field in the metric and Palatini formalisms
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Quintessential inflation in Palatini $f(R)$ gravity
• Reheating in Models with Non-minimal Coupling in metric and Palatini formalisms
• Palatini $R^2$ Quintessential Inflation
• Tachyonic Preheating in Palatini $R^2$ Inflation
• Constraints on Kinetically Modified Inflation from WMAP5
• Critical point Higgs inflation in the Palatini formulation
• Cosmological constraints on general, single field inflation
• Slow-roll inflation in Palatini $F(R)$ gravity
• On UV-completion of Palatini-Higgs inflation
• Constant-roll $k$-Inflation Dynamics
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Minimal $k$-inflation in light of the conformal metric-affine geometry
• Progress in Higgs inflation
• Reheating predictions in Gravity Theories with Derivative Coupling
• General slow-roll inflation in $f(R)$ gravity under the Palatini approach
• Preheating in Palatini Higgs inflation on the lattice
• Multiple point criticality principle and Coleman-Weinberg inflation
• On the number of $e$-folds in the Jordan and Einstein frames
• Inflation with $R_{(\alpha \beta )}$ terms in the Palatini formulation
• Extended interactions in the Palatini-$R^2$ inflation
• $k$-Inflation-corrected Einstein-Gauss-Bonnet Gravity with Massless Primordial Gravitons
• Variable Inflaton Equation of State and Reheating
• Reheating constraints on K-inflation
• Palatini approach and large-scale magnetogenesis
• Gravitino constraints on supergravity inflation

Cited by in corpus (10)

• Inflation in Metric-Affine Quadratic Gravity
• Implications of Palatini gravity for inflation and beyond
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Bimetric-Affine Quadratic Gravity
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• General Einstein-Cartan quadratic gravity with derivative couplings
• Large Field Polynomial Inflation in Palatini $f(R,\varphi )$ Gravity
• Cosmic inflation in metric-affine gravity
• Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models
• Reheating in geometric Weyl-invariant Einstein-Cartan gravity