Improved WKB analysis of cosmological perturbations

Abstract

Improved Wentzel-Kramers-Brillouin (WKB)-type approximations are presented in order to study cosmological perturbations beyond the lowest order. Our methods are based on functions which approximate the true perturbation modes over the complete range of the independent (Langer) variable, from sub-horizon to super-horizon scales, and include the region near the turning point. We employ both a perturbative Green's function technique and an adiabatic (or ``semiclassical'') expansion (for a linear turning point) in order to compute higher order corrections. Improved general expressions for the WKB scalar and tensor power spectra are derived for both techniques. We test our methods on the benchmark of power-law inflation, which allows comparison with exact expressions for the perturbations, and find that the next-to-leading order adiabatic expansion yields the amplitude of the power spectra with excellent accuracy, whereas the next-to-leading order with the perturbative Green's function method does not improve the leading order result significantly. However, in more general cases, either or both methods may be useful.

13 pages, REVTeX4 style, 5 figures, final version to appear in Phys. Rev. D

References in corpus (12)

• Reconstructing the Inflaton Potential --- an Overview
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• Semiclassicality and Decoherence of Cosmological Perturbations
• Higher order corrections to primordial spectra from cosmological inflation
• The influence of cosmological transitions on the evolution of density perturbations
• WKB approximation for inflationary cosmological perturbations
• Multiple inflation and the WMAP 'glitches'
• On the Problem of Predicting Inflationary Perturbations
• The Inflationary Perturbation Spectrum
• Characterizing Inflationary Perturbations: The Uniform Approximation
• Energy-Momentum Tensor of Cosmological Fluctuations during Inflation
• Plane waves in a general Robertson-Walker background

Cited by in corpus (39)

• Encyclopaedia Inflationaris
• Inflation after WMAP3: Confronting the Slow-Roll and Exact Power Spectra with CMB Data
• Pointer states for primordial fluctuations in inflationary cosmology
• Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations
• The Observational Status of Cosmic Inflation after Planck
• Reheating in $R^2$ Palatini inflationary models
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Inflaton field potential producing the exactly flat spectrum of adiabatic perturbations
• The exact numerical treatment of inflationary models
• K-inflationary Power Spectra in the Uniform Approximation
• 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
• Theoretical Uncertainties in Inflationary Predictions
• Higher Order Slow-Roll Predictions for Inflation
• Improved WKB analysis of Slow-Roll Inflation
• Cosmic Inflation at the Crossroads
• On the accuracy of slow-roll inflation given current observational constraints
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• Slow-Roll Inflation at N3LO
• A WKB approach to scalar fields dynamics in curved space-time
• Method of comparison equations for cosmological perturbations
• Primordial power spectrum at N3LO in effective theories of inflation
• Dynamical Properties of the Mukhanov-Sasaki Hamiltonian in the context of adiabatic vacua and the Lewis-Riesenfeld invariant
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method
• Resonant structure of space-time of early universe
• Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method
• A fully quantum method of determination of penetrability and reflection coefficients in quantum FRW model with radiation
• Clocking the End of Cosmic Inflation
• Semiclassical analysis of the Starobinsky inflationary model
• 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 Method of Comparison Equations for Schwarzschild Black Holes
• Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities
• Semiclassical analysis of the tensor power spectrum in the Starobinsky inflationary model
• Double power series method for approximating cosmological perturbations
• Quantum method of determination of penetrability in FRW model with radiation
• Quantum dynamics of evolution of flat universe in the first stage