Large and small field inflation from hyperbolic sigma models

Abstract

Long standing themes in inflation include the issue of large field vs. small field inflation as well as the question what fraction of phase space leads to sufficient inflation, and furthermore is compatible with the experimental data. In the present paper these issues are discussed in the context of modular inflation, a specialization of the framework of automorphic nonlinear $\sigma$-models associated to homogeneous spaces $G/K$ in which the continuous shift symmetry group $G$ is weakly broken to discrete subgroups $\Gamma$. The target spaces of these theories inherit a curved structure from the group $G$, which in the case of modular invariant inflation leads to a hyperbolic field space geometry. It is shown that in this class of models the symmetry structure leads to both large and small field inflationary trajectories within a single modular inflation model. The present paper analyzes the concrete model of $j$-inflation, a hyperbolic model with nontrivial inflaton interactions. It describes in some detail the structure of the initial conditions, including a systematic analysis of several phenomenological functions on the target space, leading to constraints on the curvature scalar of the field space by upcoming experiments, as well as a discussion of the scaling behavior of the spectral index, the finite volume fraction of the field space leading to sufficient inflation, the attractor behavior of $j$-inflation, and a comparison of inflaton trajectories vs. target space geodesics. The tensor-ratio analysis shows that $j$-inflation is an interesting target for upcoming ground and satellite experiments.

References in corpus (78)

• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Planck 2018 results. X. Constraints on inflation
• The Simons Observatory: Science goals and forecasts
• Hybrid Inflation
• On the Geometry of the String Landscape and the Swampland
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• The Swampland: Introduction and Review
• What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?
• How long before the end of inflation were observable perturbations produced?
• BICEP2 / Keck Array x: Constraints on Primordial Gravitational Waves using Planck, WMAP, and New BICEP2/Keck Observations through the 2015 Season
• CMB-S4 Science Case, Reference Design, and Project Plan
• CMBPol Mission Concept Study: Probing Inflation with CMB Polarization
• Trans-Planckian Censorship and the Swampland
• Trans-Planckian Censorship and Inflationary Cosmology
• The Measure Problem in Cosmology
• Inflation Physics from the Cosmic Microwave Background and Large Scale Structure
• Cosmic microwave background measurements can discriminate among inflation models
• Multi-field Conformal Cosmological Attractors
• Large Field Inflation and Double $\alpha$-Attractors
• Cosmological Attractors and Initial Conditions for Inflation
• Quantum Cosmological Perturbations: Predictions and Observations
• A Horizon Ratio Bound for Inflationary Fluctuations
• Cosmological constraints in extended parameter space from the Planck 2018 Legacy release
• Universality classes of inflation
• Hyperinflation
• Escher in the Sky
• Initial Conditions for Inflation - A Short Review
• WMAPping inflationary physics
• Measure and Probability in Cosmology
• Hybrid inflation along waterfall trajectories
• Constraining Inflation with Cosmic Microwave Background Polarization
• Inflationary predictions for scalar and tensor fluctuations reconsidered
• Primordial perturbations from inflation with a hyperbolic field-space
• Attractor Solutions in Scalar-Field Cosmology
• Universality of multi-field $\alpha$-attractors
• Eternal Inflation
• Attractor Behaviour in Multifield Inflation
• Initial Conditions for Smooth Hybrid Inflation
• Implications of the scalar tilt for the tensor-to-scalar ratio
• Hypernatural inflation
• The Lyth Bound of Inflation with a Tilt
• On the problem of initial conditions for inflation
• Hyperinflation generalised: from its attractor mechanism to its tension with the `swampland conjectures'
• Landscape tomography through primordial non-Gaussianity
• Fine tuning of the initial conditions for hybrid inflation
• CMB targets after the latest Planck data release
• Initial conditions for hybrid inflation
• Fractal initial conditions and natural parameter values in hybrid inflation
• Four-year Cosmology Large Angular Scale Surveyor (CLASS) Observations: On-sky Receiver Performance at 40, 90, 150, and 220 GHz Frequency Bands
• On the inflationary massive field with a curved field manifold
• Avoiding the blue spectrum and the fine-tuning of initial conditions in hybrid inflation
• Probing the power spectrum bend with recent CMB data
• Attractors, Bifurcations and Curvature in Multi-field Inflation
• The Search For Primordial Tensor Modes
• Hyperbolic field space and swampland conjecture for DBI scalar
• Initial Conditions for Supersymmetric Inflation
• Multi-field Inflation in High-Slope Potentials
• A Tip for Landscape Riders: Multi-Field Inflation Can Fulfill the Swampland Distance Conjecture
• Eternal Inflation, Entropy Bounds and the Swampland
• The Multi-Field, Rapid-Turn Inflationary Solution
• On backreaction effects in geometrical destabilisation of inflation
• Gravitational waves and large field inflation
• Cosmological Trans-Planckian Conjectures are not Effective
• Modular Inflation Observables and $j$-Inflation Phenomenology
• The Cosmology Large Angular Scale Surveyor Receiver Design
• A Finite Measure for the Initial Conditions of Inflation
• Initial conditions and sampling for multifield inflation
• Lyth bound revisited
• Generalized two-field $\alpha$-attractor models from geometrically finite hyperbolic surfaces
• Hidden symmetries of two-field cosmological models
• Generalized two-field $\alpha$-attractors from the hyperbolic triply-punctured sphere
• Multifield Reheating after Modular $j$-Inflation
• Modular Inflation at Higher Level $N$
• A General Framework of Automorphic Inflation
• Probing the origin of our Universe through cosmic microwave background constraints on gravitational waves
• Observational constraints on Hyperinflation
• Symmetries of stationary points of the $G$-invariant potential and the framework of the auxiliary group
• Updated Constraints on Large Field Hybrid Inflation

Cited by in corpus (1)

• Scaling behavior of observables as a model characteristic in multifield inflation