Ultraviolet Unitarity Violations in Non-minimally Coupled Scalar-Starobinsky Inflation

Abstract

We perform the calculation for tree-level ultraviolet unitarity violation scales for scalar-$R^2$ inflation models by including an additional $R^2|\Phi {|}^2$-type term. Due to certain constraints, we resort to the Einstein frame for our calculations, where we separate our analysis between metric and Palatini formulations. We follow recent works in this line that debunk the naive predictions for unitarity violations in Higgs' inflation models to determine how to accurately estimate the behaviour of scattering amplitudes in the UV limit. Later, we work out different cases by assuming potentials corresponding to known inflation scenarios so we could predict the range of coupling parameters for which the theories would remain unitary up to the Planckian regime. We also try to find the behaviour of the scattering amplitudes for these theories during the transition from inflationary to reheating epoch.

arXiv commentMajor changes: Calculation extended for general potentials with extra sections for specific inflationary scenarios; abstract and conclusions modified accordingly. Minor changes: added references; typographical errors corrected

References in corpus (49)

• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Horndeski theory and beyond: a review
• New Model of Inflation with Non-minimal Derivative Coupling of Standard Model Higgs Boson to Gravity
• On Inflation with Non-minimal Coupling
• Scalaron from $R^2$-gravity as a Heavy Field
• xPert: Computer algebra for metric perturbation theory
• Higgs inflation
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• Cosmology in generalized Proca theories
• Higgs Inflation and Naturalness
• Higgs Scalaron Mixed Inflation
• Classical and Quantum Initial Conditions for Higgs Inflation
• Inflation in the Mixed Higgs-$R^2$ Model
• A Unitarity-Conserving Higgs Inflation Model
• Reheating in $R^2$ Palatini inflationary models
• Higgs Starobinsky Inflation
• Self-healing of unitarity in Higgs inflation
• Remarks on Higgs Inflation
• Starobinsky-like two-field inflation
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Noether symmetry for non-minimally coupled fermion fields
• Primordial perturbations generated by Higgs field and $R^2$ operator
• A simple $F(\mathcal{R},\varphi )$ deformation of Starobinsky inflationary model
• Anisotropic cosmological solutions in massive vector theories
• Cosmology in beyond-generalized Proca theories
• Higgs Inflation as Nonlinear Sigma Model and Scalaron as its $\sigma$-meson
• Solving the Standard Model Problems in Softened Gravity
• 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
• On the equivalence between Starobinsky and Higgs inflationary models in gravity and supergravity
• Inflation with an antisymmetric tensor field
• Does Palatini Higgs Inflation Conserve Unitarity?
• Inflation and Reheating in f(R,h) theory formulated in the Palatini formalism
• Renormalization Group Equations of Higgs-$R^2$ Inflation
• An introduction to inflation and cosmological perturbation theory
• On Preheating in Higgs Inflation
• Perturbative Reheating in the Mixed Higgs-$R^2$ Model
• Fermion field as inflaton, dark energy and dark matter
• Higher Derivative Scalar Tensor Theory in Unitary Gauge
• Inflation with $f(R,\varphi )$ in Jordan frame
• Avoiding instabilities in antisymmetric tensor field driven inflation
• Hamiltonian Formalism for Nonlocal Gravity Models
• Gravitational waves from inflation with antisymmetric tensor field
• Covariant Effective Action for Generalized Proca Theories
• Inflation with antisymmetric tensor field: new candidates
• Hamiltonian Analysis of Nonlocal F(R) Gravity Models
• Noncanonical Approaches To Inflation

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• Implications of Palatini gravity for inflation and beyond
• Observable Primordial Gravitational Waves from Non-minimally Coupled $R^2$ Palatini Modified Gravity
• Ultraviolet Sensitivity in Higgs-Starobinsky Inflation
• Ghost Free Theory in Unitary Gauge: A New Candidate
• Cosmic inflation in metric-affine gravity
• Self-healing unitarity is an optical illusion
• Testing the Starobinsky model of inflation with resonant cavities