An analytic approach to non-slow-roll inflation

Abstract

Brief periods of non-slow-roll evolution during inflation can produce interesting observable consequences, as primordial black holes, or an inflationary gravitational wave spectrum enhanced at small scales. We develop a model independent, analytic approach for studying the predictions of single-field scenarios which include short phases of slow-roll violation. Our method is based on Taylor expanding the equations for cosmological fluctuations in a small quantity, which parameterizes the duration of the non-slow-roll eras. The super-horizon spectrum of perturbations is described by few effective parameters, and is characterized by a pronounced dip followed by a rapid growth in its amplitude, as typically found in numerical and analytical studies. The dip position $k_{\mathrm{dip}}/k_{\ast }$ and the maximal enhancement ${\Pi }_{\max }$ of the spectrum towards small scales are found to be related by the law $k_{\mathrm{dip}}/k_{\ast }\propto {\Pi }_{\max }^{-1/4}$, and we determine the proportionality constant. For a single epoch of slow-roll violation we confirm previous studies, finding that the steepest slope of the spectrum well after the dip has spectral index $n-1=4$. On the other hand, with multiple phases of slow-roll violation, the slope of the spectrum is generally enhanced. For example, when two epochs of slow-roll violation take place, separated by a phase of quasi-de Sitter expansion, we find that the spectral index can reach the value $n-1=8$. This phenomenon indicates that the slope of the spectrum keeps memory of the history of non-slow-roll phases occurred during inflation.

37 pages, 11 figures. V2: References added, small improvements made. Accepted for publication in PRD. V3: One reference added

References in corpus (16)

• Primordial Black Holes as Dark Matter
• Monodromy in the CMB: Gravity Waves and String Inflation
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
• Primordial black hole dark matter from single field inflation
• Primordial Black Holes and Slow-Roll Violation
• Gravitational waves at interferometer scales and primordial black holes in axion inflation
• Ultra slow-roll inflation demystified
• Constraints on the induced gravitational wave background from primordial black holes
• Multi-messenger Probes of Inflationary Fluctuations and Primordial Black Holes
• On the evolution of tachyonic perturbations at super-Hubble scales
• Rollercoaster Cosmology
• Attractors, Universality and Inflation
• A Phase Transition between Small and Large Field Models of Inflation
• Poly-instanton axion inflation

Cited by in corpus (48)

• Cosmology with the Laser Interferometer Space Antenna
• Inflation and Primordial Black Holes
• Anatomy of single-field inflationary models for primordial black holes
• Probing Anisotropies of the Stochastic Gravitational Wave Background with LISA
• Probing non-Gaussianities with the high frequency tail of induced gravitational waves
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Constraining Primordial Black Hole Formation from Single-Field Inflation
• Did JWST observe imprints of axion miniclusters or primordial black holes?
• Primordial Black Holes Arise When The Inflaton Falls
• Primordial Black Hole Formation in Starobinsky's Linear Potential Model
• Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation
• Primordial black holes from null energy condition violation during inflation
• Primordial black hole dark matter from inflation: the reverse engineering approach
• Non-Gaussianity in inflationary scenarios for primordial black holes
• Very Hairy Inflation
• Observational imprints of enhanced scalar power on small scales in ultra slow roll inflation and associated non-Gaussianities
• Consistency conditions and primordial black holes in single field inflation
• Enhancing gravitational wave anisotropies with peaked scalar sources
• Loop contributions to the scalar power spectrum due to quartic order action in ultra slow roll inflation
• Missing one-loop contributions in secondary gravitational waves
• One-loop infrared rescattering by enhanced scalar fluctuations during inflation
• Formation of trapped vacuum bubbles during inflation, and consequences for PBH scenarios
• Double Monodromy Inflation: A Gravity Waves Factory for CMB-S4, LiteBIRD and LISA
• Comparing sharp and smooth transitions of the second slow-roll parameter in single-field inflation
• Numerical stochastic inflation constrained by frozen noise
• Observing nulling of primordial correlations via the 21 cm signal
• The effect of multiple features on the power spectrum in two-field inflation
• CMB $\mu T$ cross-correlations as a probe of PBH scenarios
• Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes
• Sudden braking and turning with a two-field potential bump: primordial black hole formation
• Probing parity-odd bispectra with anisotropies of GW $V$ modes
• Primordial tensor bispectra in $\mu$-CMB cross-correlations
• Constraining the impact of standard model phase transitions on primordial black holes
• Constraining ultra slow roll inflation using cosmological datasets
• Global Portraits of Nonminimal Inflation: Metric and Palatini
• One-loop corrections to the E-type $\alpha$-attractor models of inflation and primordial black hole production
• Stochastic inflation with gradient interactions
• Non-Gaussianities and Primordial Black Holes
• Bayesian reconstruction of primordial perturbations from induced gravitational waves
• Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage
• High-redshift Galaxies from JWST Observations in More Realistic Dark Matter Halo Models
• An analytical approximation of the evolution of the primordial curvature perturbation in the ultraslow-roll inflation
• Generating large primordial fluctuations in single-field inflation for PBH formation
• Bayesian inference methodology for Primordial Power Spectrum reconstructions from Large Scale Structure
• Chiral gravitational waves from multi-phase magnetogenesis
• Analytic Approximations for the Primordial Power Spectrum with Israel Junction Conditions
• Primordial gravitational waves from excited states
• Primordial black holes from the perturbations in the inflaton potential in peak theory