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

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.

10 pages, more explanation and references added, version to be published in Progress of Theoretical Physics

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• Elementary Theorems Regarding Blue Isocurvature Perturbations
• The Separate Universe Approach to Soft Limits
• Second Order Perturbations During Inflation Beyond Slow-roll
• Loop Corrections to Cosmological Perturbations in Multi-field Inflationary Models
• Fermionic Isocurvature Perturbations
• The minimal curvaton-higgs model
• Non-Gaussianity in multiple three-form field inflation
• Large gauge transformation, Soft theorem, and Infrared divergence in inflationary spacetime
• CMB hemispherical asymmetry from non-linear isocurvature perturbations
• Tachyon Mediated Non-Gaussianity
• Stochastic Effects in Axion Inflation and Primordial Black Holes Formation
• Cosmological observables in multi-field inflation with a non-flat field space
• Multiple scalar particle decay and perturbation generation
• Affleck-Dine dynamics, Q-ball formation and thermalisation
• Rotating a Curvaton Brane in a Warped Throat
• Primordial curvature perturbation during and at the end of multi-field inflation
• Assisted inflation in Friedmann-Robertson-Walker and Bianchi spacetimes
• Primordial black holes from temporally enhanced curvature perturbation
• Stochastic inflation beyond slow roll: noise modelling and importance sampling
• Generating the primordial curvature perturbations in preheating
• Constraining cosmological ultra-large scale structure using numerical relativity
• Constant roll warm inflation in high dissipative regime
• Mixed Inflaton and Spectator Field Models after Planck
• Generating $\fnl$ at $\ell\lsim 60$
• δN versus covariant perturbative approach to non-Gaussianity outside the horizon in multifield inflation
• Inflationary models with a flat potential enforced by non-abelian discrete gauge symmetries
• Scalar Perturbations Through Cycles
• Inflation with non-canonical scalar fields revisited
• Evolution of the curvature perturbations during warm inflation
• Scale-dependent bias from multiple-field inflation
• Tachyon inflation in the Large-$N$ formalism
• \bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation
• Cosmological dynamics of multifield dark energy
• Generic inference of inflation models by non-Gaussianity and primordial power spectrum reconstruction
• Implications of Planck results for models with local type non-Gaussianity
• Constraining Modular Inflation in the MSSM from Giant Q-Ball Formation
• Implications of the Planck bispectrum constraints for the primordial trispectrum
• Non-Gaussianity in the inflating curvaton
• On the primordial black hole formation in hybrid inflation
• Revisiting the Minimal Chaotic Inflation Model
• Gravitino Dark Matter and Non-Gaussianity
• Precision Predictions for the Primordial Power Spectra of Scalar Potential Models of Inflation
• Quantifying the behaviour of curvature perturbations during inflation
• Gauge-invariant perturbations at second order in two-field inflation
• Eliminating the eta-problem in SUGRA Hybrid Inflation with Vector Backreaction
• Spectator field models in light of spectral index after Planck
• Lower Bound on the Garvitino Mass $m_{3/2}>O(100)$ TeV in $R$-Symmetry Breaking New Inflation
• Effect of reheating on predictions following multiple-field inflation
• Path integral for multi-field inflation
• Dark Matter in Axion Landscape
• Temporal enhancement of super-horizon curvature perturbations from decays of two curvatons and its cosmological consequences
• Quantum diffusion and large primordial perturbations from inflation
• Testing scale-invariant inflation against cosmological data
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Delta-N formalism for the evolution of the curvature perturbations in generalized multi-field inflation
• Complete Hamiltonian analysis of cosmological perturbations at all orders
• Primordial non-Gaussianity in warm inflation using $\delta N$ formalism
• Hubble multi-scalar inflation
• Power-law modulation of the scalar power spectrum from a heavy field with a monomial potential
• Position Space CMB Anomalies from Multi-Stream Inflation
• Statistics of general functions of a Gaussian field -application to non-Gaussianity from preheating-
• Matching and running sensitivity in non-renormalizable inflationary models
• Anisotropic separate universe and Weinberg's adiabatic mode
• Fractional chaotic inflation in the lights of PLANCK and BICEP2
• Effects of Light Fields During Inflation
• Scale dependence of $f_{NL}$ in N-flation
• Quadra-Spectrum and Quint-Spectrum from Inflation and Curvaton Models
• ISS-flation
• Influence of Reheating on the Trispectrum and its Scale Dependence
• Boundary Crossing in Stochastic Inflation with Critical Number of Fields
• A Smooth Landscape: Ending Saddle Point Inflation Requires Features to be Shallow
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• The lessons from the running of the tensor-to-scalar ratio
• $\alpha$-attractor-type Double Inflation
• Measuring the Energy Scale of Inflation with Large Scale Structures
• Hilltop inflation with preinflation from coupling to matter fields
• Non-Gaussianities in multi-field DBI inflation with a waterfall phase transition
• Phenomenology of the minimal inflation scenario: inflationary trajectories and particle production
• MSSM-inspired multifield inflation
• Nonlinear superhorizon curvature perturbation in generic single-field inflation
• Mixed inflaton and curvaton scenario with sneutrinos
• Exploring Two-Field Inflation in the Wess-Zumino Model
• Nonlinear curvature perturbations in an exactly soluble model of multi-component slow-roll inflation
• The primordial curvature perturbation from lattice simulations
• Curvaton and the inhomogeneous end of inflation
• Cosmological constraints on the curvaton web parameters
• Separate Universes beyond General Relativity
• Extended analysis of CMB constraints on non-Gaussianity in isocurvature perturbations
• Assisted Inflation from Geometric Tachyon
• The N-Tachyon Assisted Inflation
• Full nonlinear growing and decaying modes of superhorizon curvature perturbations
• Structure of Kähler potential for D-term inflationary attractor models
• Reconstruction of potentials of the hybrid inflation in the light of primordial black hole formation
• Modulated inflation from kinetic term
• Curvaton Dynamics Revisited
• Evolution of curvature perturbation in generalized gravity theories
• What Planck does not tell us about inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Many-field Inflation: Universality or Prior Dependence?
• Mixed non-Gaussianity in multiple-DBI inflation
• New features in curvaton model
• Cosmological Perturbations of a Quartet of Scalar Fields with a Spatially Constant Gradient
• Final Thoughts on the Power Spectra of Scalar Potential Models
• Scale-dependent CMB power asymmetry from primordial speed of sound and a generalized $\delta$N formalism
• Coupling structure of multi-field primordial perturbations
• Remote Inflation as hybrid-like sneutrino/MSSM inflation
• Supergravity and Two-Field Inflation Effects in Right-Handed Sneutrino-Modified D-term Inflation
• An update on adiabatic modes in cosmology and $\delta$N formalism
• Conservation of $\zeta$ with radiative corrections from heavy field
• Extension of local-type inequality for the higher order correlation functions
• Assisted chaotic inflation in brane-world cosmology
• Non perturbative effects of primordial curvature perturbations on the apparent value of a cosmological constant
• Exploring the inflation of $F(R)$ gravity
• Non-Gaussianity in rapid-turn multi-field inflation
• Consistency relation and inflaton field redefinition in the delta N formalism
• Effects of the imaginary inflaton component in supergravity new inflation
• Sneutrinos as Mixed Inflaton and Curvaton
• A short note on the curvature perturbation at second order
• Natural Hybrid Inflation Model with Large Non-Gaussianity
• Non-minimally assisted chaotic inflation
• Cosmic Perturbations from a Rotating Field
• Dynamics of Cosmological Perturbations in Multi-Speed Inflation
• Two-field inflation with non-minimal coupling
• Structure Formation with Two Periods of Inflation: Beyond PLaIn $\Lambda$CDM
• Non Gaussianity of General Multiple-Field Inflationary Models
• Fully non-linear equivalence of delta N and covariant formalisms
• Introduction to the number of $e$-folds in slow-roll inflation
• A numerical approach to stochastic inflation and primordial black holes
• Multi-chaotic inflation with and without spectator field
• A general proof of the equivalence between the δN and covariant formalisms
• Gravity and non-gravity mediated couplings in multiple-field inflation
• Primordial non-Gaussianity as a probe of seesaw and leptogenesis
• Spectral Index and Non-Gaussianity in Supersymmetric Hybrid Inflation
• Modulation of the waterfall by a gauge field
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Stochastic inflation with gradient interactions
• Hubble induced mass after inflation in spectator field models
• Primordial gravitational wave of BICEP2 from dynamical double hybrid inflation
• Scale and shape dependent non-Gaussianity in the presence of inflationary vector fields
• Suppressed Non-Gaussianity in the Curvaton Model
• Non-Gaussianity in two-field inflation beyond the slow-roll approximation
• Spectrum of Curvature Perturbation of Multi-field Inflation with Small-Field Potential
• Axionlike Origin of the Primordial Density Perturbation
• Gradient expansion of superhorizon perturbations in G-inflation
• Non-perturbative $\delta N$
• Covariant second-order perturbations in generalized two-field inflation
• Nonminimally Assisted Inflation: A General Analysis
• Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics
• Baryogenesis in $R^2$-Higgs Inflation: the Gravitational Connection
• From Non-trivial Geometries to Power Spectra and Vice Versa
• Cosmological perturbations from a Spectator field during inflation
• Braneworld Flux Inflation
• Covariant evolution of perturbations during reheating in two-field inflation
• Curvatons and inhomogeneous scenarios with deviation from slow-roll
• Primordial Power Spectrum and Bispectrum from Lattice Simulations of Axion-U(1) Inflation
• (Multi-field) Natural Inflation and Gravitational Waves
• Generically large nongaussianity in small multifield inflation
• Generation of perturbation after multi-field inflation
• Resolving primordial physics through correlated signatures
• Towards an Observational Appraisal of String Cosmology
• Running of scalar spectral index in multi-field inflation
• The TeV-mass curvaton
• Inflation with Stochastic Boundary
• The running curvaton
• Thermal Effects and Sudden Decay Approximation in the Curvaton Scenario
• Improving the Single Scalar Consistency Relation
• A Separate Universe Approach to Quintessence Perturbations
• Large Scale Cosmic Perturbation from Evaporation of Primordial Black Holes
• Limits on the gravity wave contribution to microwave anisotropies
• Dynamical renormalization and universality in classical multifield cosmological models
• Affleck-Dine baryogenesis with modulated reheating
• Relics of spatial curvature in the primordial non-gaussianity
• Non-Gaussianity in the Cosmic Microwave Background Induced by Dipolar Dark Matter
• Flattened Axion Monodromy Beyond Two Derivatives
• High-redshift Mini-haloes from Modulated Preheating
• $\Delta N$ Formalism and Conserved Currents in Cosmology
• What We Can Learn from the Running of the Spectral Index if no Tensors are Detected in the Cosmic Microwave Background Anisotropy
• Refined Study of Isocurvature Fluctuations in the Curvaton Scenario
• Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
• Rolling in the Modulated Reheating Scenario
• The Non-Gaussianity of Racetrack Inflation Models
• Prospects for Primordial Gravitational Waves in String Inflation
• Non-Gaussianities and Primordial Black Holes
• Delta-N Formalism for Curvaton with Modulated Decay
• Cosmic perturbations, baryon asymmetry and dark matter from the minimal supersymmetric standard model
• Constraining Modified Gravity with Large non-Gaussianities
• Hamiltonian formalism for cosmological perturbations: fixing the gauge
• CMB Cold Spot from Inflationary Feature Scattering
• Stochastic origin of primordial fluctuations in the Sky
• Entropy Perturbations in N-flation
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Testing Two-Field Inflation
• Quintom fields from chiral anisotropic cosmology
• Dynamics of Multi-Component, Multi-Field Quintessence
• Stochastic inflation with quantum and thermal noise
• Spinflation from Geometric Tachyon
• Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage
• A maximal-entropy initial state of the Universe as a microscopic description of inflation
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Primordial black holes save $R^2$ inflation
• The R-axion and non-Gaussianity
• Implementation of cosmological bounce inflation with Nojiri-Odintsov generalized holographic dark fluid
• Deriving the Inflaton in Compactified M-theory with a De Sitter Vacuum
• Non-Gaussianity in a general kind noncanonical warm inflation
• Supersymmetric hybrid inflation with a light scalar
• Surprising phenomena in a rich new class of inflationary models
• Lattice Simulation of Multi-Stream Inflation
• Scale dependences of local form non-Gaussianity parameters from a DBI isocurvature field
• Two-point correlators revisited: Fast and slow scales in multifield models of inflation
• Curvature perturbation from velocity modulation
• Escape from the swamp with spectator
• Anatomy of geometrical destabilization of inflation
• Primordial black holes from a curvaton: the role of bimodal distributions
• The quantum origin of cosmic structure: theory and observations
• Primordial non-Gaussianity in noncanonical warm inflation: three- and four-point correlations
• Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation
• Cosmological Signatures of Neutrino Seesaw Mechanism
• Phase Diagram for Nflation
• Curvaton mechanism after multi-field inflation
• Effects of Variable Newton Constant During Inflation
• On the prior dependence of constraints on the tensor-to-scalar ratio
• Evolution of the spectral index after inflation
• Primordial Black Holes and Second-order Gravitational Waves in Axion-like Hybrid Inflation
• Spectral index and running of $g_{NL}$ from an isocurvature scalar field
• Ultraviolet Sensitivity of Peccei-Quinn Inflation
• Curvature Perturbations in the Effective Field Theory of Inflation
• Uniform Rate Inflation
• 'Constraint consistency' at all orders in Cosmological perturbation theory
• Cosmological Non-Gaussianity from Neutrino Seesaw Mechanism
• Multifield curved solid: Early dark energy and perturbation instabilities
• A New Class of Non-canonical Conformal Attractors for Multifield Inflation
• de Sitter symmetries and inflationary scalar-vector models
• Sneutrinos as two inflatons and curvaton and leptogenesis
• M-flation and its spectators
• Stochastic Inflation with Interacting Noises
• Adiabatic Duality: Duality of cosmological models with varying slow-roll parameter and sound speed
• The Size of Local Bispectrum and Trispectrum in a Non-Minimal Inflation
• The validity of separate-universe approach in transient ultra-slow-roll inflation
• $\delta N$ formalism on the past light-cone
• On the coupling of vector fields to the Gauss-Bonnet invariant
• Time-reversed Stochastic Inflation
• Generalized local ansatz for scale-dependent primordial non-Gaussianities and future galaxy surveys
• Remarks on non-gaussian fluctuations of the inflaton and constancy of ζoutside the horizon
• Gravity of Cosmological Perturbations in the CMB
• Cosmon as the Modulon: Non-Gaussianity from Dark Energy
• Tilt and Tensor-to-Scalar Ratio in Multi-Scalar Field Inflation: Non-Sum-Separable Case
• Primordial non-Gaussianity in noncanonical warm inflation with nonminimal derivative coupling
• Slow-roll corrections in multi-field inflation: a separate universes approach
• $\delta N$ formalism with gradient interactions
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting
• Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta N$ formalism
• Uniform rate inflation on the brane
• $\delta n$ formalism: A new formulation for the probability density of the curvature perturbation
• Separate universe in multifield inflation: a phase-space approach
• Kinematically Blocked Curvaton
• Squeezed bispectrum from multi-field inflation with curved field space metric
• Couplings and spectra in modular inflation
• Unified Origin of Curvature Perturbation and Baryon Asymmetry of the Universe
• Sustainability of multi-field inflation and bound on string scale
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Holographic beta function in de Sitter space
• Cosmological long-wavelength solutions in non-adiabatic multi-fluid systems
• The $R^2$-Higgs inflation with two Higgs doublets
• Wronskian Formulation of the Spectrum of Curvature Perturbations
• Primordial gravitational waves from excited states
• Moment transport equations and their application to the perturbed universe
• Passive Curvaton
• Positivity vs. Lorentz-violation: an explicit example
• Towards a de Sitter quintom-like cosmology from a reduction of a 7-dimensional $BF$ theory
• Inflationary spectral tilts as a result of the dilatation symmetry breaking
• Non-Gaussianity in D3-brane inflation
• Inflationary Hubble Parameter from the Gravitational Wave Spectrum in the General Slow-roll Approximation