Frame Covariant Nonminimal Multifield Inflation

Abstract

We introduce a frame-covariant formalism for inflation of scalar-curvature theories by adopting a differential geometric approach which treats the scalar fields as coordinates living on a field-space manifold. This ensures that our description of inflation is both conformally and reparameterization covariant. Our formulation gives rise to extensions of the usual Hubble and potential slow-roll parameters to generalized fully frame-covariant forms, which allow us to provide manifestly frame-invariant predictions for cosmological observables, such as the tensor-to-scalar ratio $r$, the spectral indices $n_{\mathcal{R}}$ and $n_T$, their runnings ${\alpha }_{\mathcal{R}}$ and ${\alpha }_T$, the non-Gaussianity parameter $f_{NL}$, and the isocurvature fraction ${\beta }_{\mathrm{iso}}$. We examine the role of the field space curvature in the generation and transfer of isocurvature modes, and we investigate the effect of boundary conditions for the scalar fields at the end of inflation on the observable inflationary quantities. We explore the stability of the trajectories with respect to the boundary conditions by using a suitable sensitivity parameter. To illustrate our approach, we first analyze a simple minimal two-field scenario before studying a more realistic nonminimal model inspired by Higgs inflation. We find that isocurvature effects are greatly enhanced in the latter scenario and must be taken into account for certain values in the parameter space such that the model is properly normalized to the observed scalar power spectrum $P_{\mathcal{R}}$. Finally, we outline how our frame-covariant approach may be extended beyond the tree-level approximation through the Vilkovisky-De Witt formalism, which we generalize to take into account conformal transformations, thereby leading to a fully frame-invariant effective action at the one-loop level.

43 pages, 12 figures; some minor typos corrected; to appear in Nuclear Physics B

References in corpus (48)

• Planck 2013 results. XVI. Cosmological parameters
• The Standard Model Higgs boson as the inflaton
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• Generating the curvature perturbation without an inflaton
• Hybrid Inflation
• Planck 2013 results. XXII. Constraints on inflation
• Acoustic Signatures in the Primary Microwave Background Bispectrum
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• A new approach to the evolution of cosmological perturbations on large scales
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• The inflationary prediction for primordial non-gaussianity
• Features of heavy physics in the CMB power spectrum
• Particle physics models of inflation and curvaton scenarios
• The conformal frame freedom in theories of gravitation
• Adiabatic Modes in Cosmology
• Metric perturbations in two-field inflation
• The Effective Field Theory of Multifield Inflation
• An Observational Test of Two-field Inflation
• A review of Axion Inflation in the era of Planck
• Multifield Inflation after Planck: The Case for Nonminimal Couplings
• Question of quantum equivalence between Jordan frame and Einstein frame
• Curvature and isocurvature perturbations in two-field inflation
• Isocurvature Perturbations in Multiple Inflationary Models
• Conformal Transformations with Multiple Scalar Fields
• Cosmological perturbations from multi-field inflation in generalized Einstein theories
• Equivalence of the Einstein and Jordan frames
• Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion
• Primordial Bispectrum from Multifield Inflation with Nonminimal Couplings
• Supergravity based inflation models: a review
• Invariant quantities in the scalar-tensor theories of gravitation
• Calculating the local-type fNL for slow-roll inflation with a non-vacuum initial state
• Conformal transformations in classical gravitational theories and in cosmology
• A covariant approach to general field space metric in multi-field inflation
• The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation
• Multifield Inflation after Planck: Isocurvature Modes from Nonminimal Couplings
• A frame independent classification of single field inflationary models
• Curvaton Dynamics and the Non-Linearity Parameters in Curvaton Model
• Conformal Frame Dependence of Inflation
• Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
• Slow-roll Inflation for Generalized Two-Field Lagrangians
• Curvature perturbation in multi-field inflation with non-minimal coupling
• Multiple-field inflation and the CMB
• Non-minimal Higgs Inflation and Frame Dependence in Cosmology
• Non-Gaussian Correlations Outside the Horizon
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
• General formula for the running of local fNL
• Running of the Running and Entropy Perturbations During Inflation

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• Hidden and explicit quantum scale invariance
• Cosmology from pregeometry
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• Primordial flat frame -- a new view on inflation
• Covariant Effective Action for Antisymmetric Tensor Field
• Global Portraits of Nonminimal Inflation: Metric and Palatini
• Pole inflation from non-minimal coupling to gravity
• Nonminimally Assisted Inflation: A General Analysis
• Double inflation via non-minimally coupled spectator
• Crossing the Big Bang singularity
• Revisiting local-scale invariant gravitational theory
• The $R^2$-Higgs inflation with two Higgs doublets
• Non-perturbative approach for scalar particle production in Higgs-$R^2$ inflation