Second Order General Slow-Roll Power Spectrum

Abstract

Recent combined results from the Wilkinson Microwave Anisotropy Probe (WMAP) and Sloan Digital Sky Survey (SDSS) provide a remarkable set of data which requires more accurate and general investigation. Here we derive formulae for the power spectrum P(k) of the density perturbations produced during inflation in the general slow-roll approximation with second order corrections. Also, using the result, we derive the power spectrum in the standard slow-roll picture with previously unknown third order corrections.

11 pages, 1 figure ; A typo in Eq. (38) is fixed ; References expanded and a note added

References in corpus (20)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Cosmological parameters from SDSS and WMAP
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• The 3D power spectrum of galaxies from the SDSS
• 4-Year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results
• A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background
• DASI First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• Galaxy Clustering in Early SDSS Redshift Data
• Cosmology from Maxima-1, Boomerang and COBE/DMR CMB Observations
• A High Spatial Resolution Analysis of the MAXIMA-1 Cosmic Microwave Background Anisotropy Data
• Cosmological Parameter Extraction from the First Season of Observations with DASI
• The Density Perturbation Power Spectrum to Second-Order Corrections in the Slow-Roll Expansion
• Constraining slow-roll inflation with WMAP and 2dF
• The Spectrum of Density Perturbations produced during Inflation to Leading Order in a General Slow-Roll Approximation
• WMAP and Inflation
• The Power Spectrum for a Multi-Component Inflaton to Second-Order Corrections in the Slow-Roll Expansion
• Scale Dependent Spectral Index in Slow Roll Inflation
• Cosmological Perturbations with Multiple Scalar Fields

Cited by in corpus (82)

• Planck 2013 results. XXII. Constraints on inflation
• Encyclopaedia Inflationaris
• The Anatomy of Electro-Weak Symmetry Breaking. I: The Higgs boson in the Standard Model
• Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyon: Unified analyses
• Inflation after WMAP3: Confronting the Slow-Roll and Exact Power Spectra with CMB Data
• Non-Gaussianity from Step Features in the Inflationary Potential
• Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations
• The Observational Status of Cosmic Inflation after Planck
• Generalized Slow Roll for Large Power Spectrum Features
• Large slow-roll corrections to the bispectrum of noncanonical inflation
• Inflation with moderately sharp features in the speed of sound: GSR and in-in formalism for power spectrum and bispectrum
• Fast Computation of Bispectrum Features with Generalized Slow Roll
• Warp Features in DBI Inflation
• Localized correlated features in the CMB power spectrum and primordial bispectrum from a transient reduction in the speed of sound
• Generalized Slow Roll for Non-Canonical Kinetic Terms
• Inflationary Steps in the Planck Data
• Cosmological constraints on slow-roll inflation: an update
• Breaking scale invariance from a singular inflaton potential
• Bispectrum in Single-Field Inflation Beyond Slow-Roll
• On the scalar consistency relation away from slow roll
• Precision of Inflaton Potential Reconstruction from CMB Using the General Slow-Roll Approximation
• A New delta N Formalism for Multi-Component Inflation
• New constraints on the observable inflaton potential from WMAP and SDSS
• Inflationary Perturbations and Precision Cosmology
• Inflation and reheating in scale-invariant scalar-tensor gravity
• The Importance of Slow-roll Corrections During Multi-field Inflation
• Inflationary signatures of single-field models beyond slow-roll
• Correlating correlation functions of primordial perturbations
• Limits on primordial power spectrum resolution: An inflationary flow analysis
• Holography, Diffeomorphisms, and Scaling Violations in the CMB
• Constraining Inflation
• Constraints on inflation with LSS surveys: features in the primordial power spectrum
• Searching for primordial localized features with CMB and LSS spectra
• Cosmic Inflation at the Crossroads
• Inflation Model Selection meets Dark Radiation
• CMB Constraints on Principal Components of the Inflaton Potential
• Complete WMAP Constraints on Bandlimited Inflationary Features
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• Slow-Roll Inflation at N3LO
• Searching for features of a string-inspired inflationary model with cosmological observations
• Lensing anomaly and oscillations in the primordial power spectrum
• General formula for the running of local fNL
• Polarization Predictions for Inflationary CMB Power Spectrum Features
• End of multi-field inflation and the perturbation spectrum
• Observational constraints on tachyon and DBI inflation
• Nonlinear Excitations in Inflationary Power Spectra
• Running from Features: Optimized Evaluation of Inflationary Power Spectra
• From the Spectrum to Inflation : An Inverse Formula for the General Slow-Roll Spectrum
• Fast Computation of First-Order Feature-Bispectrum Corrections
• Blue running of the primordial tensor spectrum
• Second Order Perturbations During Inflation Beyond Slow-roll
• Parameterizing the Power Spectrum: Beyond the Truncated Taylor Expansion
• Multiple scalar particle decay and perturbation generation
• Fine Features in the Primordial Power Spectrum
• Modular thermal inflation without slow-roll approximation
• The lessons from the running of the tensor-to-scalar ratio
• Generalized Slow Roll for Tensors
• Scalar Bispectrum Beyond Slow-Roll in the Unified EFT of Inflation
• Quantum quenches during inflation
• Can power spectrum observations rule out slow-roll inflation?
• Generation of perturbation after multi-field inflation
• From Non-trivial Geometries to Power Spectra and Vice Versa
• From the Spectrum to Inflation: A Second Order Inverse Formula for the General Slow-Roll Spectrum
• Dark energy in hybrid inflation
• Reconstruction and exact solutions for cosmological perturbations from a generalized gravity theory
• Inflation in minimal left-right symmetric model with spontaneous D-parity breaking
• Troubles for observing the inflaton potential
• Scale invariance of the primordial tensor power spectrum
• Shapes and features of the primordial bispectrum
• Clocking the End of Cosmic Inflation
• Superimposed Oscillations in Brane Inflation
• Potential reconstruction from general power spectrum in single-field inflation
• Non-linear effects in early Universe cosmology
• Cross-tests of CMB features in the primordial spectra
• Mimicking two field inflationary features with a single field
• Renormalisation of non-differentiable potentials
• Higher order non-linear parameters with PLANCK
• Wronskian Formulation of the Spectrum of Curvature Perturbations
• Aspects of inflation and the very early universe
• Minimal gauge inflation
• Inflationary Hubble Parameter from the Gravitational Wave Spectrum in the General Slow-roll Approximation
• The Black Hole Window on Cosmic Inflation