Strong Coupling Problem with Time-Varying Sound Speed

Abstract

For a single scalar field with unit sound speed minimally coupled to Einstein gravity, there are exactly three distinct cosmological solutions which produce a scale invariant spectrum of curvature perturbations in a dynamical attractor background, assuming vacuum initial conditions: slow-roll inflation; a slowly contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation of state; and an adiabatic ekpyrotic phase on a slowly expanding background. Of these three, only inflation remains weakly coupled over a wide range of modes, the other scenarios can produce at most 12 e-folds of scale invariant and gaussian modes. In this paper, we investigate how allowing the speed of sound of fluctuations to evolve in time affects this classification. While in the presence of a variable sound speed there are many more scenarios which are scale invariant at the level of the two-point function, they generically suffer from strong coupling problems similar to those in the canonical case. There is, however, an exceptional case with superluminal sound speed, which suppresses non-gaussianities and somewhat alleviates strong coupling issues. We focus on a particular realization of this limit and show these scenarios are constrained and only able to produce at most 28 e-folds of scale invariant and gaussian perturbations. A similar bound should hold more generally --- the condition results from the combined requirements of matching the observed amplitude of curvature perturbations, demanding that the Hubble parameter remain sub-Planckian and keeping non-gaussianities under control. We therefore conclude that inflation remains the unique scenario, assuming a single degree of freedom on an attractor background, capable of producing arbitrarily many scale invariant modes while remaining weakly coupled. Alternative mechanisms must inevitably be unstable or rely on multiple degrees of freedom.

23 pages, 1 figure, v2: minor edits, version to appear in PRD

References in corpus (25)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• New Ekpyrotic Cosmology
• Generating Ekpyrotic Curvature Perturbations Before the Big Bang
• The Measure Problem in Cosmology
• Tensor Modes from a Primordial Hagedorn Phase of String Cosmology
• String Gas Cosmology and Structure Formation
• Non-Gaussianities in New Ekpyrotic Cosmology
• Simple Bounds from the Perturbative Regime of Inflation
• Speedy sound and cosmic structure
• On the Initial Conditions in New Ekpyrotic Cosmology
• Curvature perturbations from ekpyrotic collapse with multiple fields
• More on the Spectrum of Perturbations in String Gas Cosmology
• Generating Scale-Invariant Perturbations from Rapidly-Evolving Equation of State
• Scale-Invariance and the Strong Coupling Problem
• Dark Energy and the Return of the Phoenix Universe
• Near Scale Invariance with Modified Dispersion Relations
• Non-Gaussianity in single field models without slow-roll
• Towards a Cosmological Dual to Inflation
• Bimetric structure formation: non-Gaussian predictions
• General conditions for scale-invariant perturbations in an expanding universe
• A Briefing on the Ekpyrotic/Cyclic Universe
• Scale Invariance via a Phase of Slow Expansion
• On Primordial Density Perturbation and Decaying Speed of Sound
• Flow in Cyclic Cosmology

Cited by in corpus (12)

• DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
• Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe
• A Galileon Design of Slow Expansion: II
• Matter bounce cosmology with a generalized single field: non-Gaussianity and an extended no-go theorem
• Cuscuton gravity as a classically stable limiting curvature theory
• Reconstruction of a Nonminimal Coupling Theory with Scale-invariant Power Spectrum
• Primordial non-Gaussianity from Galilean Genesis without strong coupling problem
• Reconstructing the EFT of Inflation from Cosmological Data
• Horizon-preserving dualities and perturbations in non-canonical scalar field cosmologies
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• Can non-local or higher derivative theories provide alternatives to inflation?
• The four fixed points of scale invariant single field cosmological models