Higgs-$R^2$ inflation -- full slow-roll study at tree-level

Abstract

We consider Higgs inflation with an $\alpha R^2$ term. It adds a new scalar degree of freedom, which leads to a two-field model of inflation. We do a complete slow-roll analysis of the three-dimensional parameter space of the $R^2$ coefficient $\alpha$, the non-minimal coupling $\xi$ and the Higgs self-coupling $\lambda$. We find three classes of inflationary solutions, but only pure $R^2$ and attractor solutions fit observations. We find that pure Higgs inflation is impossible when the $R^2$ term is present regardless of how small $\alpha$ is. However, we can have Higgs-like inflation, where the amplitude of the perturbations does not depend on $\alpha$ and the predictions as a function of e-folds are the same as in Higgs inflation, although the inflationary trajectory is curved in field space. The spectral index is $0.939<n_R<0.967$, and constraining it to the observed range, the tensor-to-scalar ratio varies from $3.8\times 10^{-3}$ to the maximum allowed by observations, $0.079$. Observational constraints on isocurvature perturbations contribute to these limits, whereas non-Gaussianity is automatically in the range allowed by observations.

arXiv commentv2. Added references, corrected numerical analysis of inflationary trajectories. Range of values for the spectral index narrowed down. v3. Added references and clarified text, fixed typos. Published version. 18 pages, 5 figures

References in corpus (68)

• f(R) Theories Of Gravity
• The Standard Model Higgs boson as the inflaton
• Higgs inflation: consistency and generalisations
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
• On the Naturalness of Higgs Inflation
• Power-counting and the Validity of the Classical Approximation During Inflation
• Comment on Higgs Inflation and Naturalness
• Metric-affine f(R) theories of gravity
• On Inflation with Non-minimal Coupling
• Primordial Black Hole production in Critical Higgs Inflation
• Scalaron from $R^2$-gravity as a Heavy Field
• Higgs inflation at the critical point
• Higgs inflation still alive
• Living beyond the edge: Higgs inflation and vacuum metastability
• Higgs-Palatini Inflation and Unitarity
• Higgs inflation from Standard Model criticality
• Higgs Inflation and Naturalness
• Higgs Scalaron Mixed Inflation
• Classical and Quantum Initial Conditions for Higgs Inflation
• Gravitational corrections to Standard Model vacuum decay
• Higgs inflation with loop corrections in the Palatini formulation
• Violent Preheating in Inflation with Nonminimal Coupling
• Palatini inflation in models with an $R^2$ term
• Inflation with $R^2$ term in the Palatini formalism
• Inflation in the Mixed Higgs-$R^2$ Model
• Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton inflations
• A Unitarity-Conserving Higgs Inflation Model
• Higgs Starobinsky Inflation
• On the robustness of the primordial power spectrum in renormalized Higgs inflation
• Planck scale black hole dark matter from Higgs inflation
• Preheating after Higgs Inflation: Self-Resonance and Gauge boson production
• Distinguishing between R^2-inflation and Higgs-inflation
• Self-healing of unitarity in Higgs inflation
• Preheating after multifield inflation with nonminimal couplings, III: Dynamical spacetime results
• The Decay of the Standard Model Higgs after Inflation
• Combined Preheating on the lattice with applications to Higgs inflation
• Higgs xi-inflation for the 125-126 GeV Higgs: a two-loop analysis
• On the violent preheating in the mixed Higgs-$R^2$ inflationary model
• From stable to unstable anomaly-induced inflation
• Higgs inflation at the hilltop
• Starobinsky-like two-field inflation
• Higgs Gravitational Interaction, Weak Boson Scattering, and Higgs Inflation in Jordan and Einstein Frames
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• UV (in)sensitivity of Higgs inflation
• Minimal Higgs inflation
• Primordial perturbations generated by Higgs field and $R^2$ operator
• Late and early time phenomenology of Higgs-dependent cutoff
• Frame Covariant Nonminimal Multifield Inflation
• Nonminimal Coleman--Weinberg Inflation with an $R^2$ term
• Inflation in an effective gravitational model & asymptotic safety
• Gravitational Interaction of Higgs Boson and Weak Boson Scattering
• Unitarity-violation in Generalized Higgs Inflation Models
• Initial Conditions for Critical Higgs Inflation
• Planck mass and inflation as consequences of dynamically broken scale invariance
• Two-loop corrections to Starobinsky-Higgs inflation
• Electroweak relaxation of cosmological hierarchy
• 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
• The Problem with False Vacuum Higgs Inflation
• Unitarity and predictiveness in new Higgs inflation
• Observational signatures of Higgs inflation
• Uniqueness of the gauge invariant action for cosmological perturbations
• Preheating the Universe from the Standard Model Higgs
• Hillclimbing inflation
• Hillclimbing Higgs inflation
• Higgs inflation and vacuum stability

Cited by in corpus (20)

• Higgs inflation with the Holst and the Nieh-Yan term
• Dynamically induced Planck scale and inflation in the Palatini formulation
• Tracing the high energy theory of gravity: an introduction to Palatini inflation
• Trans-Planckian Censorship, Inflation and Dark Matter
• BICEP/Keck and Cosmological Attractors
• Constant-roll in the Palatini-$R^2$ models
• Critical point Higgs inflation in the Palatini formulation
• Initial conditions for plateau inflation: a case study
• Enhanced Curvature Perturbation and Primordial Black Hole Formation in Two-stage Inflation with a break
• Scalaron-Higgs inflation reloaded: Higgs-dependent scalaron mass and primordial black hole dark matter
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Renormalization Group Equations of Higgs-$R^2$ Inflation
• Perturbative Reheating in the Mixed Higgs-$R^2$ Model
• The Higgs field and early universe cosmology: a (brief) review
• Natural-Scalaron Inflation
• Higgs field in cosmology
• Warm Higgs-Starobinsky inflation
• Starobinksy Inflation, Gravitational Contact Terms and the Induced BEH Boson Mass
• Primordial black holes formation in inflationary $F(R)$ models with scalar fields
• On Inflation and Reheating Features in the Higgs-$R^2$ Model