A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation

1995/07/31 by M. Sasaki, Misao Sasaki, Ewan D. Stewart +1 · 146 citations
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #Geophysics and Gravity Measurements #Relativity and Gravitational Theory #astro-ph #gr-qc #hep-ph

paper · pdf · doi:10.1143/ptp.95.71

published as Prog.Theor.Phys.95:71-78,1996 · 10 pages, more explanation and references added, version to be published in Progress of Theoretical Physics

arxiv created 1995/11/29 · crossref issued 1996/01/01 · crossref published 1996/01/01 · crossref published-print 1996/01/01 · openalex publication_date 1996/01/01 · crossref created 2005/02/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · crossref deposited 2017/08/24 · crossref indexed 2026/07/29 · openalex updated_date 2026/07/31

Abstract

The standard calculation of the spectrum of density perturbations produced during inflation assumes that there is only one real dynamical degree of freedom during inflation. However, there is no reason to believe that this is actually the case. In this paper we derive general analytic formulae for the spectrum and spectral index of the density perturbations produced during inflation.

Cited by

• Spectator Axions in String Inflation and Primordial Black Holes
• Nonlinear lattice framework for inflation: Bridging stochastic inflation and the δN formalism
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting
• Trispectrum in Extended USR Model with Transition to SR
• Heavy Field Effects on Inflationary Models in Light of ACT Data
• Stochastic inflation with gradient interactions
• Extending the Dynamical Systems Toolkit: Coupled Fields in Multiscalar Dark Energy
• Stochastic Inflation with Interacting Noises
• Waterfall phase in supersymmetric hybrid inflation
• Primordial Black Holes Save R² Inflation
• Stochastic inflation as a superfluid
• δn formalism: A new formulation for the probability density of the curvature perturbation
• FIVE-YEARWILKINSON MICROWAVE ANISOTROPY PROBEOBSERVATIONS: COSMOLOGICAL INTERPRETATION
• Isotropy, anisotropies and non-Gaussianity in the scalar-induced gravitational-wave background: diagrammatic approach for primordial non-Gaussianity up to arbitrary order
• STOchastic LAttice Simulation of hybrid inflation
• Primordial black holes and their gravitational-wave signatures
• Inflation dynamics and reheating
• The inflationary Hubble parameter from the gravitational wave spectrum in the general slow-roll approximation
• Non-Gaussian Curvature Spikes from Chaotic Billiards in Inflation Preheating
• Inflationary models with a flat potential enforced by non-Abelian discrete gauge symmetries
• Multifield Dirac-Born-Infeld inflation and non-Gaussianities
• Non-Gaussianity of Racetrack Inflation Models
• Primordial curvature fluctuation and its non-Gaussianity in models with modulated reheating
• Dynamics of a large extra dimension inspired hybrid inflation model
• Modulated perturbations from instant preheating after new ekpyrosis
• Scale-invariant perturbations from chaotic inflation
• Supergravity and two-field inflation effects in right-handed sneutrino-modified D-term inflation
• N-flation
• N-flation from multiple DBI type actions
• Assisted tachyonic inflation
• On the Issue of theζseries convergence and loop corrections in the generation of observable primordial non-Gaussianity in slow-roll inflation. II. The trispectrum
• Non-Gaussianity from massless preheating
• Large non-Gaussianities with intermediate shapes from quasi-single-field inflation
• Non-Gaussianity and cosmic uncertainty in curvaton-type models
• Couplings and spectra in modular inflation
• Density fluctuations in thermal inflation and non-Gaussianity
• Scale dependence of localfNL
• Non-Gaussianity from resonant curvaton decay
• Primordial statistical anisotropy generated at the end of inflation
• Signatures of non-Gaussianity in the curvaton model
• Anisotropic Bispectrum of Curvature Perturbations from Primordial Non-Abelian Vector Fields
• One-loop graviton corrections to the curvature perturbation from inflation
• Spinflation from geometric tachyon
• Non-Gaussian perturbations from multi-field inflation
• Generation of perturbation after multi-field inflation
• Assisted inflation
• Loop corrections to cosmological perturbations in multi-field inflationary models
• Parametric amplification of metric fluctuations during reheating in two field models
• ISS-flation
• High-redshift minihaloes from modulated preheating
• Elliptic inflation: generating the curvature perturbation without slow-roll
• Generating the Curvature Perturbation at the End of Inflation in String Theory
• Perturbation spectra of “N-flation”
• Non-Gaussianity and gravitational waves from a quadratic and self-interacting curvaton
• Statistical anisotropy of the curvature perturbation from vector field perturbations
• Primordial perturbations from inflation with a hyperbolic field-space
• The importance of slow-roll corrections during multi-field inflation
• Braneworld flux inflation
• Large scale structure from the Higgs fields of the supersymmetric standard model
• THE N-TACHYON ASSISTED INFLATION
• What does inflation really predict?
• Inflation models and observation
• Supersymmetric hybrid inflation with a light scalar
• Calculating nonadiabatic pressure perturbations during multifield inflation
• The R-axion and non-Gaussianity
• A geometric description of the non-Gaussianity generated at the end of multi-field inflation
• δNversus covariant perturbative approach to non-Gaussianity outside the horizon in multifield inflation
• Analysis of the evolution of curvature perturbations in preheating by using δ N formalism
• Primordial trispectrum from inflation
• Multiple Field Inflation
• Evolution of the curvature perturbations during warm inflation
• Gravitino dark matter and non-Gaussianity
• Density fluctuations from warm inflation
• Successful modular cosmology
• Inflationary physics from the Wilkinson Microwave Anisotropy Probe
• N-flation: Non-Gaussianity in the horizon-crossing approximation
• More varieties of hybrid inflation
• Generating the cosmic microwave background power asymmetry withgNL
• Curvaton with nonminimal derivative coupling to gravity
• The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation
• Short distance physics and the consistency relation for scalar and tensor fluctuations in the inflationary universe
• General formula for the running of local fNL
• Gravitational waves and the scale of inflation
• Curvature perturbation spectra from waterfall transition, black hole constraints and non-Gaussianity
• Time-reversed Stochastic Inflation
• Constant-Roll Inflation
• Reconstruction of potentials of hybrid inflation in the light of primordial black hole formation
• Ultra-slow-roll inflation with quantum diffusion
• Inflation in String Theory
• Power-law modulation of the scalar power spectrum from a heavy field with a monomial potential
• Hyperinflation generalised: from its attractor mechanism to its tension with the ‘swampland conditions’
• Cosmological observables in multi-field inflation with a non-flat field space
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• Inflation in multi-field modified DBM potentials
• Formation of primordial black holes from non-Gaussian perturbations produced in a waterfall transition
• Hilltop inflation
• Horizon crossing and inflation with largeη
• Non-Gaussianity, spectral index, and tensor modes in mixed inflaton and curvaton models
• δMformalism: a new approach to cosmological perturbation theory in anisotropic inflation
• On reaching the adiabatic limit in multi-field inflation
• Anisotropic separate universe and Weinberg's adiabatic mode
• Non-Gaussianity Consistency Relation for Multifield Inflation
• Modulated inflation from the kinetic term
• Vector curvaton without instabilities
• The separate universe approach to soft limits
• The matter bounce curvaton scenario
• Numerical evaluation of the bispectrum in multiple field inflation—the transport approach with code
• An extended matter bounce scenario: current status and challenges
• Primordial black holes from inflation and non-Gaussianity
• The effective field theory of multifield inflation
• New approach to the evolution of cosmological perturbations on large scales
• Primordial black holes and local non-Gaussianity in canonical inflation
• Revisiting non-Gaussianity from non-attractor inflation models
• Inhomogeneous non-gaussianity
• Inflation in the mixed Higgs-R2 model
• A bound concerning primordial non-Gaussianity
• Primordial black holes and gravitational waves from resonant amplification during inflation
• Non-Gaussianity and baryonic isocurvature fluctuations in the curvaton scenario
• Preheating from target space curvature and unitarity violation: Analysis in field space
• Tachyon inflation in the large-Nformalism
• On the generation of a non-gaussian curvature perturbation during preheating
• Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation
• Combined local and equilateral non-Gaussianities from multifield DBI inflation
• Measurement of primordial non-Gaussianity using the WMAP 5-year temperature skewness power spectrum
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• A short note on the curvature perturbation at second order
• Multi-disformal invariance of non-linear primordial perturbations
• Primordial non-Gaussianity in multi-scalar slow-roll inflation
• Multiple inflation and the WMAP “glitches”
• Quantum diffusion during inflation and primordial black holes
• Stochastic inflation beyond slow roll
• Critical Number of Fields in Stochastic Inflation
• Implications of the Planck bispectrum constraints for the primordial trispectrum
• Light Scalar Fields Foster Production of Primordial Black Holes
• Spectral index and non-Gaussianity in supersymmetric hybrid inflation
• The running curvaton *
• On classification of models of large local-type non-Gaussianity
• Enhancement of primordial curvature perturbations in R³-corrected Starobinsky-Higgs inflation
• Robust non-minimal attractors in many-field inflation
• Conserved cosmological perturbations
• Non-Gaussianity in curvaton models with nearly quadratic potentials
• Four-year COBE normalization of inflationary cosmologies
• Primordial bispectrum from multifield inflation with nonminimal couplings
• Testing two-field inflation
• Primordial black holes from a curvaton: the role of bimodal distributions
• On the Hamilton-Jacobi approach to inflation beyond slow roll