Nonminimal Coleman--Weinberg Inflation with an $R^2$ term

Abstract

We extend the Coleman--Weinberg inflationary model where a scalar field $\varphi$ is non-minimally coupled to gravity with the addition of the $R^2$ term. We express the theory in terms of two scalar fields and going to the Einstein frame we employ the Gildener--Weinberg formalism, compute the one-loop effective potential and essentially reduce the problem to the case of single-field inflation. It turns out that there is only one free parameter, namely, the mixing angle between the scalars. For a wide range of this angle, we compute the inflationary observables which are in agreement with the latest experimental bounds. The effect of the $R^2$ term is that it lowers the value of the tensor-to-scalar ratio $r$.

arXiv commenttypos fixed, equation (3.16) and discussion around it added, updated references

References in corpus (73)

• Modified Gravity and Cosmology
• f(R) theories
• Extended Theories of Gravity
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• 1/R gravity and Scalar-Tensor Gravity
• Scalar-tensor gravity in an accelerating universe
• Agravity
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Scalaron from $R^2$-gravity as a Heavy Field
• Scale invariance, unimodular gravity and dark energy
• Higgs-Dilaton Cosmology: From the Early to the Late Universe
• Dynamically Induced Planck Scale and Inflation
• Towards Completing the Standard Model: Vacuum Stability, EWSB and Dark Matter
• Inflationary universe from perfect fluid and $F(R)$ gravity and its comparison with observational data
• Higgs Scalaron Mixed Inflation
• Inflation and Dark Matter in the Higgs Portal of Classically Scale Invariant Standard Model
• Constraints from Inflation on Scalar-Tensor Gravity Theories
• Palatini inflation in models with an $R^2$ term
• Higgs-Dilaton Cosmology: an effective field theory approach
• Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory
• Inflation in the Mixed Higgs-$R^2$ Model
• Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton inflations
• Invariant quantities in the scalar-tensor theories of gravitation
• Dark energy, inflation and dark matter from modified F(R) gravity
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Higgs Starobinsky Inflation
• Scale-Independent Inflation and Hierarchy Generation
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Inflationary $\alpha$-attractors from $F(R)$ Gravity
• Evolution of Structures in Generalized Gravity Theories
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Inflationary Perturbations in No-Scale Theories
• New universal attractor in nonmininally coupled gravity: Linear inflation
• On the geometrical interpretation of scale-invariant models of inflation
• Starobinsky-like two-field inflation
• Constant-Roll (Quasi-)Linear Inflation
• Inflation from Broken Scale Invariance
• Primordial perturbations generated by Higgs field and $R^2$ operator
• Inflation and reheating in theories with spontaneous scale invariance symmetry breaking
• Inflation in a scale invariant universe
• Frame Covariant Nonminimal Multifield Inflation
• Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
• Reconstructing the inflationary $f(R)$ from observations
• Linear inflation from quartic potential
• Non-minimal CW inflation, electroweak symmetry breaking and the 750 GeV anomaly
• Super-Heavy Dark Matter - Towards Predictive Scenarios from Inflation
• Minimal but non-minimal inflation and electroweak symmetry breaking
• Classically Scale Invariant Inflation, Supermassive WIMPs, and Adimensional Gravity
• Natural Inflation with Hidden Scale Invariance
• Evolving Planck Mass in Classically Scale-Invariant Theories
• Two-loop corrections to Starobinsky-Higgs inflation
• Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints
• Electroweak relaxation of cosmological hierarchy
• Transformation properties and general relativity regime in scalar-tensor theories
• Inflation and reheating in scale-invariant scalar-tensor gravity
• Frame-invariant approach to higher-dimensional scalar-tensor gravity
• The simplest extension of Starobinsky inflation
• Reinterpretation of the Starobinsky model
• Scalar-tensor linear inflation
• Invariant quantities in the multiscalar-tensor theories of gravitation
• Origin of inflation in CFT driven cosmology: $R^2$-gravity and non-minimally coupled inflaton models
• Disentangling the $f(R)$ - Duality
• Conformal Transformations and Weak Field Limit of Scalar-Tensor Gravity
• Inflation as a spontaneous symmetry breaking of Weyl symmetry
• Generalized Slow Roll Conditions and the Possibility of Intermediate Scale Inflation in Scalar-Tensor Theory
• Multi-field effects in a simple extension of $R^2$ inflation
• Equations of motion in scalar-tensor theories of gravity: A covariant multipolar approach
• Reheating and preheating in the simplest extension of Starobinsky inflation
• Saddle point inflation from higher order corrections to Higgs/Starobinsky inflation
• Attractor Models in Scalar-Tensor Theories of Inflation
• On the Cosmological Frame Problem
• Some remarks concerning invariant quantities in scalar-tensor gravity

Cited by in corpus (46)

• 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
• Tracing the high energy theory of gravity: an introduction to Palatini inflation
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Weyl $R^2$ inflation with an emergent Planck scale
• Quasi-Conformal Models and the Early Universe
• Dimensional Transmutation in Gravity and Cosmology
• GUT Physics in the era of the LHC
• Scale independent $R^2$ inflation
• Planck mass and inflation as consequences of dynamically broken scale invariance
• Towards distinguishing variants of non-minimal inflation
• $R^p$ Attractors Static Neutron Star Phenomenology
• Higgs inflation and teleparallel gravity
• Universal Inflationary Attractors Implications on Static Neutron Stars
• Inflationary Attractors Predictions for Static Neutron Stars in the Mass-Gap Region
• Static Neutron Stars Perspective of Quadratic and Induced Inflationary Attractor Scalar-tensor Theories
• Initial conditions for plateau inflation: a case study
• Enhanced Curvature Perturbation and Primordial Black Hole Formation in Two-stage Inflation with a break
• Slow-roll inflation in Palatini $F(R)$ gravity
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Higgs-$R^2$ inflation -- full slow-roll study at tree-level
• Non-minimal (self-)running inflation: metric vs. Palatini formulation
• Multiple point criticality principle and Coleman-Weinberg inflation
• Scale-invariant inflation with one-loop quantum corrections
• Unified Emergence of Energy Scales and Cosmic Inflation
• Inflation in Weyl-invariant Einstein-Cartan gravity
• Integrable modified gravity cosmological models with an additional scalar field
• A Walking Dilaton Inflation
• Gravitational wave constraints on the observable inflation
• Superpotential method for $F(R)$ cosmological models
• Generalized $R^p$-attractor Cosmology in the Jordan and Einstein Frames: New Type of Attractors and Revisiting Standard Jordan Frame $R^p$ Inflation
• Scale Invariant Gravity and Black Hole Ringdown
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Gravitational Coleman-Weinberg Mechanism
• Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory
• Inflation with Massive Spin-2 Ghosts
• Minima of Classically Scale-Invariant Potentials
• Inflation and dark matter after spontaneous Planck scale generation by hidden chiral symmetry breaking
• Gravitational Waves from Preheating in Inflation with Weyl Symmetry
• Quantum gravitational corrections to the inflationary power spectra in scalar-tensor theories
• Palatini Higgs and Coleman-Weinberg inflation with non-minimal coupling
• On Conformal Transformation with Multiple Scalar Fields and Geometric Property of Field Space with Einstein-like Solutions
• Dynamically induced spin-2 mass in a Weyl-invariant framework
• Large Field Polynomial Inflation in Palatini $f(R,\varphi )$ Gravity
• Constraining the inflaton potential with gravitational waves from oscillons