Observational Signatures and Non-Gaussianities of General Single Field Inflation

Abstract

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.

53 pages, 5 figures; v3, minor revision, JCAP version; v4, numerical coefficients corrected in Appendix B, discussion on consistency condition revised

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• Cosmology of the Tachyon in Brane Inflation
• Cosmological Evolution of Dirac-Born-Infeld Field
• Brane Inflation is Attractive
• Inflationary potentials in DBI models
• Non-Gaussian inflationary shapes in $G^3$ theories beyond Horndeski
• Slow-Roll Inflation at N3LO
• The Power of Locality: Primordial Non-Gaussianity at the Map Level
• Warm DBI inflation with constant sound speed
• Statistical Anisotropy from Vector Curvaton in D-brane Inflation
• Observational Signatures of Gravitational Couplings in DBI Inflation
• Tensors, non-Gaussianities, and the future of potential reconstruction
• Large fluctuations and Primordial Black Holes
• What Can We Learn by Combining the Skew Spectrum and the Power Spectrum?
• Large Local Non-Gaussianity from General Single-field Inflation
• Transporting non-Gaussianity from sub to super-horizon scales
• Constraints on anisotropic primordial non-Gaussianity from intrinsic alignments of SDSS-III BOSS galaxies
• Consistency relations for sharp features in the primordial spectra
• Toward evading the strong coupling problem in Horndeski genesis
• Vanishing of local non-Gaussianity in canonical single field inflation
• Soft limits in holographic cosmology
• Multi-disformal invariance of nonlinear primordial perturbations
• Minimizing gravitational lensing contributions to the primordial bispectrum covariance
• Primordial Non-Gaussianity from G-inflation
• Visible sector inflation and the right thermal history in light of Planck data
• DBI N-flation
• The structure of correlation functions in single field inflation
• Fluid Inflation
• Secondary non-Gaussianity and Cross-Correlation Analysis
• Curvature Perturbations from a Massive Vector Curvaton
• Primordial Non-Gaussianity Estimation using 21 cm Tomography from the Epoch of Reionization
• Enhanced CMBR non-Gaussianities from Lorentz violation
• One-loop corrections to the power spectrum in general single-field inflation
• On the Initial State and Consistency Relations
• Three-form inflation and non-Gaussianity
• A Consistency Relation for Single-Field Inflation with Power Spectrum Oscillations
• Effective Field Theory of non-Attractor Inflation
• Searching for non-Gaussianity in the WMAP data
• Relations between canonical and non-canonical inflation
• Curvaton with Nonminimal Derivative Coupling to Gravity II: Full Perturbation Analysis
• Single-Field Inflation After WMAP5
• The effect of non-Gaussian curvature perturbations on the formation of primordial black holes
• Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach
• Stochastic non-attractor inflation
• Constraining Scale-Dependent Non-Gaussianity with Future Large-Scale Structure and the CMB
• Primordial tensor non-Gaussianities from general single-field inflation with non-Bunch-Davies initial states
• Non-local self-healing of Higgs inflation
• Large Deviations in the Early Universe
• Tachyon inflation with steep potentials
• General and consistent statistics for cosmological observations
• DBI Inflation using a One-Parameter Family of Throat Geometries
• Gravitational Wave Constraints on Multi-Brane Inflation
• Warped Wilson Line DBI Inflation
• Bispectra from two-field inflation using the long-wavelength formalism
• Non-Gaussianities in Collider Energy Flux
• de Sitter swampland bound in the Dirac-Born-Infeld inflation model
• Les Houches lectures on inflationary observables and string theory
• Can non-minimal coupling restore the consistency condition in bouncing universes?
• Why Must Primordial Non-Gaussianity Be Very Small?
• Probing the initial state of inflation: analytical structure of cosmological correlators
• Consistency relation in power law G-inflation
• Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology
• Spectral Index in Curvaton Scenario
• Quantum entanglement in cosmology
• There and Back Again: Mapping and Factorising Cosmological Observables
• Probing a stationary non-Gaussian background of stochastic gravitational waves with pulsar timing arrays
• Consistency Relation for multifield inflation scenario with all loop contributions
• Modifications to Cosmological Power Spectra from Scalar-Tensor Entanglement and their Observational Consequences
• Small-scale Tests of Inflation
• New Shapes of Primordial Non-Gaussianity from Quasi-Single Field Inflation with Multiple Isocurvatons
• Inflation on an Open Racetrack
• Inflation with $0\le c_{\mathrm{s}}\le 1$
• Resurrecting the Power-law, Intermediate, and Logamediate Inflations in the DBI Scenario with Constant Sound Speed
• Why should primordial perturbations be in a vacuum state?
• Constraints on Primordial non-Gaussianity from Future HI Intensity Mapping Experiments
• Correlating CMB Spectral Distortions with Temperature: what do we learn on Inflation?
• Numerical evaluation of the three-point scalar-tensor cross-correlations and the tensor bi-spectrum
• Bispectrum from open inflation
• On Cross-correlations between Curvature and Isocurvature Perturbations during Inflation
• Hemispherical Anomaly from Asymmetric Initial States
• Generalized non-local $R^2$-like inflation
• Anisotropies in Scalar-Induced Gravitational-Wave Background from Inflaton-Curvaton Mixed Scenario with Sound Speed Resonance
• Minimal cut-off vacuum state constraints from CMB bispectrum statistics
• Non-Gaussianity from Lifshitz Scalar
• Enhanced Inflation in the Dirac-Born-Infeld framework
• Local non-Gaussianity from rapidly varying sound speeds
• Unifying Inflation with early and late Dark Energy in Multi-Fields: Spontaneously broken scale invariant TMT
• CMB constraints on running non-Gaussianity
• Constraints on general primordial non-Gaussianity using wavelets for the Wilkinson Microwave anisotropy probe 7-year data
• Anatomy of bispectra in general single-field inflation -- modal expansions
• Inflation with Massive Vector Fields
• Gravitational waves from fermion production during axion inflation
• Inflation in DBI models with constant gamma
• The scale-dependent signature of primordial non-Gaussianity in the large-scale structure of cosmic reionization
• DBI Galileon in the Effective Field Theory of Inflation: Orthogonal non-Gaussianities and constraints from the Trispectrum
• Inflationary gravitational waves in the effective field theory of modified gravity
• Primordial Spikes from Wrapped Brane Inflation
• Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum
• The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation
• Nonlocal Inflation
• Loop Corrections to Cosmological Perturbations in Multi-field Inflationary Models
• Tilt and Running of Cosmological Observables in Generalized Single-Field Inflation
• Fields Annihilation and Particles Creation in DBI inflation
• Primordial non-Gaussianities of gravitational waves beyond Horndeski
• Tachyon Mediated Non-Gaussianity
• Non-Gaussianities in models of inflation with large and negative entropic masses
• The scalar bi-spectrum during preheating in single field inflationary models
• A geometric bound on F-term inflation
• Non-Gaussianity in multiple three-form field inflation
• Preheating with the Brakes On: The Effects of a Speed Limit
• Rotating a Curvaton Brane in a Warped Throat
• The Komatsu Spergel Wandelt estimator for oscillations in the cosmic microwave background bispectrum
• Enhanced local-type inflationary trispectrum from a non-vacuum initial state
• Sharp inflaton potentials and bi-spectra: Effects of smoothening the discontinuity
• A Self-gravitating Dirac-Born-Infeld Global Monopole
• Origin of structure: Statistical characterization of the primordial density fluctuations and the collapse of the wave function
• General CMB bispectrum analysis using wavelets and separable modes
• Observational constraints on assisted k-inflation
• Varying Alpha Driven by the Dirac-Born-Infeld Scalar Field
• Optimal computation of anisotropic galaxy three point correlation function multipoles using 2DFFTLOG formalism
• Analytic Formulae for Inflationary Correlators with Dynamical Mass
• Primordial non-Gaussianities in single field inflationary models with non-trivial initial states
• Scale-dependent bias from multiple-field inflation
• Universality in generalized models of inflation
• Primordial Non-Gaussianity from a Joint Analysis of Cosmic Microwave Background Temperature and Polarization
• Holographic non-Gaussianities in general single-field inflation
• Mimetic Inflation
• Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function, and halo bias from the path-integral excursion set method
• On the Trispectrum of Galileon Inflation
• On the initial condition of inflationary fluctuations
• Production of non-gaussianities in a bouncing phase
• Cosmology with Persistent Homology: a Fisher Forecast
• Scalar induced gravitational waves from Chern-Simons gravity during inflation era
• Non-Gaussianity as a signature of thermal initial condition of inflation
• Anisotropic non-Gaussianity from Rotational Symmetry Breaking Excited Initial States
• The Degeneracy Problem in Non-Canonical Inflation
• Numerical evaluation of inflationary 3-point functions on curved field space
• Strong Coupling Problem with Time-Varying Sound Speed
• New DBI Inflation model with Kinetic Coupling to Einstein Gravity
• Path integral for multi-field inflation
• Non-Bunch-Davies Anisotropy
• Primordial power spectrum features in phenomenological descriptions of inflation
• Planck Limits on Non-canonical Generalizations of Large-field Inflation Models
• Primordial non-Gaussianity in noncanonical warm inflation
• Magnetogenesis and the primordial non-gaussianity
• A Modal Approach to the Numerical Calculation of Primordial non-Gaussianities
• The Odd-Parity Galaxy Bispectrum
• Perturbative unitarity in quasi-single field inflation
• Bounce from Inflation
• Anisotropic constant-roll inflation for the Dirac-Born-Infeld model
• Gauge-invariant perturbations at second order in two-field inflation
• Tachyon inflation in the holographic braneworld
• Cosmological cutting rules for Bogoliubov initial states
• Trispectrum versus Bispectrum in Single-Field Inflation
• G-inflation: From the intermediate, logamediate and exponential models
• Constraining the WMAP9 bispectrum and trispectrum with needlets
• Non-commutative Geometry Modified Non-Gaussianities of Cosmological Perturbation
• Angular bispectrum and trispectrum of scalar-induced gravitational waves: all contributions from primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$
• Confronting brane inflation with Planck and pre-Planck data
• Consistency relations in multi-field inflation
• Non-Gaussianities in multi-field DBI inflation with a waterfall phase transition
• Nonlinear superhorizon perturbations of non-canonical scalar field
• An analytic approach to perturbations from an initially anisotropic universe
• Measuring the Energy Scale of Inflation with Large Scale Structures
• Let Effective Field Theory of Inflation flow: stochastic generation of models with red/blue tensor tilt
• Quadra-Spectrum and Quint-Spectrum from Inflation and Curvaton Models
• Primordial Non-Gaussianity in Supersolid Inflation
• Mimetic DBI Inflation in Confrontation with Planck2018 data
• Inflationary Adler Conditions
• Power Spectrum and Non-Gaussianities in Anisotropic Inflation
• Revisiting non-Gaussianity of multiple-field inflation from the field equation
• Non-Gaussianities in a two-field generalization of Natural Inflation
• Differentiating G-inflation from String Gas Cosmology using the Effective Field Theory Approach
• Scale-dependent hemispherical asymmetry from general initial state during inflation
• Constraints on brane inflation after Planck 2015: Impacts of the latest local measurement of the Hubble constant
• Galileon intermediate inflation
• Non-Gaussian Shape Recognition
• Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
• Dirac-Born-Infeld and k-inflation: the CMB anisotropies from string theory
• Large Non-Gaussianity in Slow-Roll Inflation
• Embedding DBI inflation in scalar-tensor theory
• Probing signatures of bounce inflation with current observations
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• $f(\bar{R},L(X))$-gravity in the context of dark energy with power law expansion and energy conditions
• CMB imprints of non-canonical anisotropic inflation
• Non-Gaussian Shape Discrimination with Spectroscopic Galaxy Surveys
• Mixed non-Gaussianity in multiple-DBI inflation
• Consistency relations for large scale structures with primordial non-Gaussianities
• Why does the effective field theory of inflation work?
• Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field
• Adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation
• Non-Gaussian Signatures from the Postinflationary Early Universe
• Stability of a viable non-minimal bounce
• Scalar Bispectrum Beyond Slow-Roll in the Unified EFT of Inflation
• Non-Gaussianity and gravitational wave background in curvaton with a double well potential
• Non-Gaussianity in multi-sound-speed disformally coupled inflation
• Chaotic Inflation and Reheating in Generalized Scalar-Tensor Gravity
• Reconstructing the EFT of Inflation from Cosmological Data
• On primordial trispectrum from exchanging scalar modes in general multiple field inflationary models
• Alternative approach to the Starobinsky model for inflation scenarios
• Scale-dependent CMB power asymmetry from primordial speed of sound and a generalized $\delta$N formalism
• Lyth Bound, eternal inflation and future cosmological missions
• A weak lensing view on primordial non-Gaussianities
• Cosmology in nonlocal gravity
• Reconstructing Single Field Inflationary Actions From CMBR Data
• Anisotropic non-gaussianity with noncommutative spacetime
• Observational constraints on warm quasi-exponential inflation
• On Quantum Simulation Of Cosmic Inflation
• Inflationary Twin Models
• Effective Field Theory of Anisotropic Inflation and Beyond
• Study in the noncanonical domain of Goldstone inflation
• Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory
• Collapsing scenarios of K-essence generalized Vaidya spacetime under $f(\bar{R},\bar{T})$ gravity
• Effect of intermediate Minkowskian evolution on CMB bispectrum
• Resonant non-Gaussianity with equilateral properties
• Fully non-linear equivalence of delta N and covariant formalisms
• Dynamics of Cosmological Perturbations in Multi-Speed Inflation
• Jump in fluid properties of inflationary universe to reconcile scalar and tensor spectra
• Scale-dependent Bias from the Reconstruction of Non-Gaussian Distributions
• Non-canonical kinetic structures in the swampland
• The Trispectrum in the Effective Theory of Inflation with Galilean symmetry
• Testing gravity with non-Gaussianity
• Constraining primordial non-Gaussianity with cosmological weak lensing: shear and flexion
• Non-Gaussianities in the Extended EFT of Inflation
• DBI Inflation and Warped Black Holes
• Non-Gaussianity from Entanglement During Inflation
• Generic 3-point Statistics with Tensor Modes in Light of Swampland and TCC
• Impact of Instrumental Systematics on the CMB Bispectrum
• Covariant second-order perturbations in generalized two-field inflation
• More on loops in reheating: Non-gaussianities and tensor power spectrum
• Tachyon Mimetic Inflation as an Instabilities-Free Model
• Towards an Observational Appraisal of String Cosmology
• Quantum Entanglement in Multi-field Inflation
• Covariant evolution of perturbations during reheating in two-field inflation
• Non-perturbative $\delta N$
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• 1/R Correction to Gravity in the Early Universe
• Probing the Primordial Universe using Massive Fields
• Galactic Halos and Black Holes in Non-Canonical Scalar Field Theories
• Twisted Inflation
• Schwinger-Keldysh mechanism in extended quasi single field inflation
• A note on second-order perturbations of non-canonical scalar fields
• Model-Independent Signatures of New Physics in non-Gaussianity
• Analytical Insights into Constant-Roll Condition: Extending the Paradigm to Non-Canonical Models
• The Trispectrum as a Diagnostic of Primordial Orthogonal non-Gaussianities
• The Physical Content of Long Tensor Modes in Cosmology
• Flattened Axion Monodromy Beyond Two Derivatives
• Looking for non-Gaussianity in all the right places: A new basis for non-separable bispectra
• Some Aspects of the Tachyon Inflation with Superpotential in Confrontation with Planck2018 Data
• Non-Gaussianities in DBI inflation with angular motion
• Relics of spatial curvature in the primordial non-gaussianity
• Constraints on Single-Field Inflation
• Non-Gaussianities in generalized non-local $R^2$-like inflation
• Non-gaussianities for primordial black hole formation
• Non-Gaussianity in the warm k-inflation
• Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries
• A New Extension of Hořava-Lifshitz Gravity and Curing Pathologies of the Scalar Graviton
• Constraints on the primordial gravitational waves with variable sound speed from current CMB data
• Principal Components of CMB non-Gaussianity
• Clocking the End of Cosmic Inflation
• B-modes and the sound speed of primordial fluctuations
• Lecture notes on non-Gaussianity
• Constraining Modified Gravity with Large non-Gaussianities
• Shapes and features of the primordial bispectrum
• Quantitative classicality in cosmological interactions during inflation
• Enhanced (p)reheating in DBI Inflation
• The interplay of CMB temperature lensing power reconstruction with primordial non-Gaussianity of local type
• Non-Gaussian statistics of de Sitter spectators: A perturbative derivation of stochastic dynamics
• Non-Linear Resonance in Relativistic Preheating
• Unitarity at Infinity and Topological Holography
• The spatial gauge-dependence of single-field inflationary bispectra
• Generating large primordial fluctuations in single-field inflation for PBH formation
• Supersymmetric Dirac-Born-Infeld Axionic Inflation and Non-Gaussianity
• Primordial Non-Gaussianity from LAMOST Surveys
• K-inflation: the legitimacy of classical treatment
• Optimal bispectrum constraints on single-field models of inflation
• CMB statistical anisotropies of classical and quantum origins
• DBI Lifshitz Inflation
• Non-Gaussian signatures of Tachyacoustic Cosmology
• Power Law and Logarithmic Ricci Dark Energy Models in Horava-Lifshitz Cosmology
• High Energy Physics and Cosmology at the Unification Frontier: Opportunities and Challenges in the coming years
• Strongly Coupled Sectors in Inflation: Gapless Theories and Unparticles
• Consistency of a kind of general noncanonical warm inflation
• Consistency relation for the Lorentz invariant single-field inflation
• Influence of Unobservable Modes on Correlation Functions during Inflation
• Attractor Solutions in Tachyacoustic Cosmology
• Degeneracy in the spectrum and bispectrum among featured inflaton potentials
• Generalizing the Swampland: Embedding $P(X,\phi )$ Inflationary Theories in a Curved Multi-field Space
• Inflation in string theory confronts data/Les modèles d'inflation en théorie des cordes face aux observations
• Anisotropic power-law inflation for models of non-canonical scalar fields non-minimally coupled to a two-form field
• Connections between Minkowski and Cosmological Correlation Functions
• Classical branches and entanglement structure in the wavefunction of cosmological fluctuations
• Probing Inflation with Precision Bispectra
• Topological Echoes of Primordial Physics in the Universe at Large Scales
• Confronting Inflation Models with the Coming Observations on Primordial Gravitational Waves
• Observational Viability of the Intermediate DBI Inflation in the Presence of a Minimal Length
• Cosmological consequences of statistical inhomogeneity
• Constraints on primordial non-Gaussianity from Planck PR4 data
• Loops in inflation with strongly non-geodesic motion
• Neural Network Reconstruction of Non-Gaussian Initial Conditions from Dark Matter Halos
• The primordial non-Gaussianities for non-singular Horndeski cosmologies
• Constraints on the Sharpness of the Curvature Power Spectrum
• Superimposed Oscillations in Brane Inflation
• Constraining Inflationary Scenarios with Braneworld Models and Second Order Cosmological Perturbations
• Derivative Interactions during Inflation: A Systematic Approach
• CMB constraints on noncommutative geometry during inflation
• Generic analysis of kinetically driven inflation
• Hamiltonian formalism of cosmological perturbations and higher derivative theories
• Primordial non-Gaussianity in noncanonical warm inflation: three- and four-point correlations
• QCD Axions and CMB Anisotropy
• Operator Method and Recursion Relations for Inflationary Correlator
• String Loop Moduli Stabilisation and Cosmology in IIB Flux Compactifications
• Consistency Relation and Non-Gaussianity in a Galileon Inflation
• Intermediate and Power-Law Inflation in the Tachyon Model with Constant Sound Speed
• Unifying inflationary and reheating solution
• The scalar-scalar-tensor inflationary three-point function in the axion monodromy model
• Inflation driven by scalar field and solid matter
• Effective Field Theory for Inflation
• A Match Made in Heaven: Linking Observables in Inflationary Cosmology
• Scalar parity-odd trispectrum from gravitational Chern-Simons interaction vertices
• A Proposal for Constraining Initial Vacuum by CMB
• Breaking the degeneracy of non-canonical quartic inflation by reheating considerations
• Viable Intermediate Inflation in the Mimetic DBI Model
• The double-soft limit in cosmological correlation functions and graviton exchange effects
• Cosmological correlation functions in scalar and vector inflationary models
• Correlation of isocurvature perturbation and non-Gaussianity
• Adiabatic Duality: Duality of cosmological models with varying slow-roll parameter and sound speed
• Numerical evaluation of the tensor bispectrum in two field inflation
• The running of featureful primordial power spectra
• Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• Disformal transformations as a change of units
• Cosmological Perturbations in Inflationary Models with Anisotropic Space-Time Scaling in Lifshitz Background
• Stochastic gravitational wave background anisotropies from inflation with non-Bunch-Davies states
• Testing a Two Field Inflation Beyond the Slow-Roll Approximation
• Tilt and Tensor-to-Scalar Ratio in Multi-Scalar Field Inflation: Non-Sum-Separable Case
• Remarks on non-gaussian fluctuations of the inflaton and constancy of ζoutside the horizon
• Schrödinger field theory in curved spacetime: In-In formalism and three-point function for inflationary background
• Revisiting the Chern-Simons interaction during inflation with a non-canonical pseudo-scalar
• Measuring CMB non-Gaussianity as a probe of Inflation and Cosmic Strings
• Inflationary predictions at small gamma
• Cosmic inflation in non-perturbative quantum gravity
• Power Spectrum Emulators from Neural Networks and Tree-Based Methods
• On the four-dimensional effective theories in brane-worlds
• Inflationary cross-correlations of a non-minimal spectator and their soft limits
• Non-perpetual Eternal Inflation and the Emergent de Sitter Swampland Conjecture
• Primordial magnetic non-Gaussianity with generic vacua and detection prospects in CMB spectral distortions
• Non-Gaussianity and finite length inflation
• Primordial black hole formation in k-inflation models
• Constraints on non-canonical chaotic inflation from ACT DR6 and BICEP/Keck data
• Probing single-field inflation: predictions, constraints, and theoretical viewpoints
• Weakly Broken Galileon Symmetry in Cosmology
• Revisiting the angular momentum growth of protostructures evolved from non-Gaussian initial conditions
• The Black Hole Window on Cosmic Inflation
• Ringing Non-Gaussianity from inflation with a step in the second derivative of the potential
• Inhomogeneous Reheating Scenario with DBI fields
• Modification from Noncommutative Inflation
• Non-Gaussianity in Cosmology: from Inflation to the CMB
• Integrated Markov Chain Monte Carlo (MCMC) analysis of primordial non-Gaussianity (f_NL) in the recent CMB data
• Quijote PNG: The information content of the halo power spectrum and bispectrum
• Recent results and perspectives on cosmology and fundamental physics from microwave surveys
• Primordial gravitational waves from excited states
• A Tail of Eternal Inflation
• Cosmological three-coupled scalar theory for the dS/LCFT correspondence
• Non-Gaussian Signatures of a Thermal Big Bang