Higher Order Slow-Roll Predictions for Inflation

Abstract

We study the WKB approximation beyond leading order for cosmological perturbations during inflation. To first order in the slow-roll parameters, we show that an improved WKB approximation leads to analytical results agreeing to within 0.1% with the standard slow-roll results. Moreover, the leading WKB approximation to second order in the slow-roll parameters leads to analytical predictions in qualitative agreement with those obtained by the Green's function method.

Replaced to match published version

References in corpus (13)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Interpretation of the TT and TE Angular Power Spectrum Peaks
• CBR Anisotropy and the Running of the Scalar Spectral Index
• Higher order corrections to primordial spectra from cosmological inflation
• Cosmological parameter estimation and the inflationary cosmology
• The Density Perturbation Power Spectrum to Second-Order Corrections in the Slow-Roll Expansion
• WKB approximation for inflationary cosmological perturbations
• A comparison of cosmological Boltzmann codes: are we ready for high precision cosmology?
• The Inflationary Perturbation Spectrum
• Characterizing Inflationary Perturbations: The Uniform Approximation
• Improved WKB analysis of cosmological perturbations
• Inflationary Perturbations and Precision Cosmology

Cited by in corpus (32)

• Encyclopaedia Inflationaris
• Inflation after WMAP3: Confronting the Slow-Roll and Exact Power Spectra with CMB Data
• The Observational Status of Cosmic Inflation after Planck
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Reheating in $R^2$ Palatini inflationary models
• The exact numerical treatment of inflationary models
• Compatibility of Planck and BICEP2 in the Light of Inflation
• K-inflationary Power Spectra at Second Order
• Exact Mapping between Tensor and Most General Scalar Power Spectra
• Backreaction and Stochastic Effects in Single Field Inflation
• Inflation and reheating in scale-invariant scalar-tensor gravity
• Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
• Improved WKB analysis of Slow-Roll Inflation
• Cosmic Inflation at the Crossroads
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• Slow-Roll Inflation at N3LO
• Fast Bayesian inference for slow-roll inflation
• A WKB approach to scalar fields dynamics in curved space-time
• Method of comparison equations for cosmological perturbations
• Power spectra and spectral indices of $k$-inflation: high-order corrections
• Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace Examples
• Tensor Bounds on the Hidden Universe
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Logarithmic divergences in the $k$-inflationary power spectra computed through the uniform approximation
• Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method
• Troubles for observing the inflaton potential
• Clocking the End of Cosmic Inflation
• Computation of the Power Spectrum in Chaotic $1/4\lambda {\varphi }^4$ Inflation
• Study of scalar and tensor power spectra in the generalized Starobinsky inflationary model using semiclassical methods
• The Upper Bound on the Tensor-to-Scalar Ratio Consistent with Quantum Gravity
• Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities
• Time-reversed Stochastic Inflation