Reconstructing the Inflaton Potential --- an Overview

Abstract

We review the relation between the inflationary potential and the spectra of density (scalar) perturbations and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest-order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. We demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. We also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation which will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and we survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. We then briefly assess the prospects for future observations reaching the quality required, and consider a simulated data set that is motivated by this outlook.

69 pages standard LaTeX plus 4 postscript figures. Postscript version of text in landscape format (35 pages) available at http://star-www.maps.susx.ac.uk/papers/infcos_papers.html Modifications are a variety of updates to discussion and references

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• Cosmic 21-cm Fluctuations as a Probe of Fundamental Physics
• Dynamically Generated Inflationary Lambda-CDM
• Quantum slow-roll and quantum fast-roll inflationary initial conditions: CMB quadrupole suppression and further effects on the low CMB multipoles
• Running of the Spectral Index in Noncommutative Inflation
• Galileon intermediate inflation
• Large Blue Spectral Isocurvature Spectral Index Signals Time-Dependent Mass
• An Observational Test of Holographic Inflation
• Constraints on Models with a Break in the Primordial Power Spectrum
• Observational constraints on the energy scale of inflation
• Constraints on the small scale curvature perturbation using Planck-2015 data
• Primordial fluctuations without scalar fields
• Pitfalls of a power-law parameterization of the primordial power spectrum for Primordial Black Hole formation
• Approximate Consistency Condition from Running Spectral Index in Slow-Roll Inflationary Models
• Quantum gravitational signatures in next-generation gravitational wave detectors
• Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field
• Lambda-inflation and CMB anisotropy
• Bianchi V inflation in the Brans-Dicke theory?
• Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation
• The cosmological principle in theories with torsion: The case of Einstein-Cartan-Dirac-Maxwell gravity
• Hysteresis in the Sky
• The History of Inflation from Microwave Background Polarimetry and Laser Interferometry
• Coupling of gravity to matter, spectral action and cosmic topology
• The Inflationary Energy Scale in Braneworld Cosmology
• Warm-polytropic inflationary universe model
• Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method
• Connecting Cosmic Inflation to Particle Physics with LiteBIRD, CMB-S4, EUCLID and SKA
• A Solution to the Graceful Exit Problem in Pre-Big Bang Cosmology
• Hamilton-Jacobi approach for quasi-exponential inflation: predictions and constraints after Planck 2015 results
• Effect of the length of inflation on angular TT and TE power spectra in power-law inflation
• Final Thoughts on the Power Spectra of Scalar Potential Models
• Reconstructing Single Field Inflationary Actions From CMBR Data
• Lyth Bound, eternal inflation and future cosmological missions
• Some Connections between Quantum Tunneling and Inflation
• Cosmological data and indications for new physics
• Is asymptotically safe inflation eternal?
• Observational constraint on the fourth derivative of the inflaton potential
• Introduction to the number of $e$-folds in slow-roll inflation
• Inflation driven by massive vector fields with derivative self-interactions
• Expectations for Inflationary Observables: Simple or Natural?
• Probing the primordial power spectra with inflationary priors
• The consistency relation in braneworld inflation
• Slow-roll inflation from massive vector fields non-minimally coupled to gravity
• Enhanced power spectra from multi-field inflation
• Initial condition of scalar perturbation in inflation
• Radiative Corrections from Heavy Fast-Roll Fields during Inflation
• Estimation of Inflation parameters for Perturbed Power Law model using recent CMB measurements
• The CWKB particle production and classical condensate in de Sitter spacetime
• Constraints on the primordial power spectrum of small scales using the neutrino signals from the dark matter decay
• Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models
• Friedmann inflation in Horava-Lifshitz gravity with a scalar field
• Cosmology Solved? Maybe
• Inflation with $f(R,\varphi )$ in Jordan frame
• Logarithmic divergences in the $k$-inflationary power spectra computed through the uniform approximation
• Anisotropic inflation in non-minimal kinetic coupling model
• Observational Status of Tachyon Natural Inflation and Reheating
• Higgs inflation model with non-minimal coupling in hybrid Palatini approach
• Reconstruction of $\alpha$-attractor supergravity models of inflation
• Slow-roll inflation without fine-tuning
• Non-minimal Higgs inflation within holographic cosmology
• The effect of quantum decoherence on inflationary gravitational waves
• Inflationary equilibrium configurations of scalar-tensor theories of gravity
• S-dual Inflation and the String Swampland
• Graviton backreaction on the local cosmological expansion in slow-roll inflation
• Consistency of Tachyacoustic Cosmology with de Sitter Swampland Conjectures
• On the dissipative non-minimal braneworld inflation
• Inflationary scenarios with scale-invariant spectral tensorial index
• Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r
• Primordial perturbations and inflation in holographic cosmology
• Towards an Observational Appraisal of String Cosmology
• A bulk inflaton from large volume extra dimensions
• Minimal-supersymmetric extended inflation field in Horava-Lifshitz gravity
• From the Spectrum to Inflation: A Second Order Inverse Formula for the General Slow-Roll Spectrum
• New Inflation vs. Chaotic Inflation, Higher Degree Potentials and the Reconstruction Program in light of WMAP3
• From Non-trivial Geometries to Power Spectra and Vice Versa
• Tachyon Mimetic Inflation as an Instabilities-Free Model
• Impacts on Cosmological Constraints from Degeneracies
• Remark on approximation in the calculation of the primordial spectrum generated during inflation
• Some Aspects of the Tachyon Inflation with Superpotential in Confrontation with Planck2018 Data
• Constant-roll Inflation in Brane Induced Gravity Cosmology
• Cosmological consequences of a scalar field with oscillating equation of state. III. Unifying inflation with dark energy and small tensor-to-scalar ratio
• Double inflation via non-minimally coupled spectator
• Slow-roll inflationary senario in the maximally extended background
• More accurate slow-roll approximations for inflation in scalar-tensor theories
• Limits on the gravity wave contribution to microwave anisotropies
• Dynamics of Potentials in Bianchi Type Scalar-Tensor Cosmology
• Testing Inflation: A Bootstrap Approach
• Duality linking standard and tachyon scalar field cosmologies
• Testing an Ansatz for the Leading Secular Loop Corrections from Quantum Gravity during Inflation
• Troubles for observing the inflaton potential
• Schwinger-Keldysh mechanism in extended quasi single field inflation
• One Extension to Explain Them All, One Scale-Invariant Spectrum to Test Them All, and in One Model Bind Them
• Constant-roll inflation driven by a scalar field with non-minimal derivative coupling
• Inflation with a constant ratio of scalar and tensor perturbation amplitudes
• Improving the Single Scalar Consistency Relation
• Slow-roll reconstruction for running spectral index
• Evolution of high-frequency gravitational waves in some cosmological models
• Breaking parity: the case of the trispectrum from chiral scalar-tensor theories of gravity
• Statistical physics of the inflaton decaying in an inhomogeneous random environment
• Stochastic inflation with quantum and thermal noise
• Cosmology of fermionic dark energy coupled to curvature
• Cosmological Perturbations without Inflation
• Gravitational Waves generated during inflation from a 5D vacuum theory of gravity in a de Sitter expansion
• Qualitative analysis of a scalar-tensor theory with exponential potential
• Suppressing the primordial tensor amplitude without changing the scalar sector in quadratic curvature gravity
• Inflation with mixed helicities and its observational imprint on CMB
• Possibly Large Corrections to the Inflationary Observables
• No slow-roll inflation à la Generalized Chaplygin Gas in General Relativity
• Lowering the self-coupling of the scalar field in a generalized Higgs inflation
• Accelerating Universes from Short-Range Interactions
• Using the Crab Nebula as a high precision calibrator for Cosmic Microwave Background polarimeters
• Hamilton-Jacobi formalism for k-inflation
• Gravitational waves in a cyclic Universe: resilience through cycles and vacuum state
• Inflation in String Field Theory
• Natural inflation with natural number of e-foldings
• Inflation model building with an accurate measure of e-folding
• CMB and LSS constraints on a single-field model of inflation
• Stabilization of Starobinsky-Vilenkin stochastic inflation by an environmental noise
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity
• False vacuum energy dominated inflation with large $r$ and the importance of ${\kappa }_s$
• Cosmic Strings and Quintessence
• Potential reconstruction from general power spectrum in single-field inflation
• Inflation
• Observational Viability of the Intermediate DBI Inflation in the Presence of a Minimal Length
• 'Constraint consistency' at all orders in Cosmological perturbation theory
• Eigenvalues of the Stewart-Lyth equation for inflation with a blue spectrum
• The Scalar-Tensor Inflationary Cosmology
• More on the Non-Gaussianity of Perturbations in a Non-Minimal Inflationary Model
• The Dynamics of Brane-World Cosmological Models
• Genus statistics on CMB polarization maps and cosmological parameters degeneracy
• Viable Anisotropic Inflation and Reheating in the Tachyon Model
• Inflation in a scalar-vector-tensor theory
• Black holes and gravitational waves in concert - a probe of superstring cosmology
• Primordial Gravitational Waves in Quadratic Gravity
• Non-adiabatic primordial fluctuations
• Consistency Relation and Non-Gaussianity in a Galileon Inflation
• Constant-roll inflation with tachyon field in the holographic braneworld
• Impact of reionization history on constraining primordial gravitational waves in future all-sky cosmic microwave background experiments
• Intermediate and Power-Law Inflation in the Tachyon Model with Constant Sound Speed
• The fate of Quasi-Exponential inflation in the light of ACT-DR6
• Superheavy Dark Matter and Parametric Resonance
• Natural Inflation from 5D SUGRA and Low Reheat Temperature
• Radiation Driven Inflation
• Primordial perturbations and inflation in a holography inspired Gauss-Bonnet cosmology
• Approximate Likelihood Approaches for Detecting the Influence of Primordial Gravitational Waves in Cosmic Microwave Background Polarization
• Quantum Gravity Effects on the Tachyon Inflation from Thermodynamic Perspective
• Imprints of cosmic strings on the cosmological gravitational wave background
• Higgs-Squark-Slepton Inflation from the MSSM
• Scalar and tensor perturbation in vacuum inflation
• An Inflationary Equation of State
• The Size of Local Bispectrum and Trispectrum in a Non-Minimal Inflation
• Viable Intermediate Inflation in the Mimetic DBI Model
• Generalized Slow-roll Inflation in Non-minimally Coupled Theories
• Clarifying Inflation Models: the Precise Inflationary Potential from Effective Field Theory and the WMAP data
• Kinetic dominance and the wavefunction of the universe
• Primordial Gravitational Waves and Reheating in a New Class of Plateau-like Inflationary Potentials
• Testing a Two Field Inflation Beyond the Slow-Roll Approximation
• $\beta$-function reconstruction of Palatini inflationary attractors
• Moduli Dynamics in Effective Nested Warped Geometry in Four Dimensions and Some Cosmological Implications
• A new approach to the vacuum of inflationary models
• From WMAP to Planck: Exact reconstruction of 4- and 5-dimensional inflationary potential from high precision CMB measurements
• Constraint on the Higgs-Dilaton potential via Warm inflation in Two-Time Physics
• Influence of the deviation of the matter power spectrum at small scales on the global 21-cm signal at cosmic dawn
• Cosmic Microwave Background Tests of Inflation
• Chaotic Inflation from the MSSM Along Flat $D$-Term Trajectory
• Logamediate inflation in DGP cosmology driven by a non-canonical scalar field
• Unified Model for Inflation and Dark Matter
• Revisiting the calculations of inflationary perturbations
• Exploring trans-Planckian physics and the curvature effect by primordial power spectrum with WMAP five-year data
• Primordial Perturbations Including Second-Order Derivatives of the Inflationary Potential
• Confronting Mukhanov Parametrization of Inflationary Equation-of-State with ACT-DR6
• Reconstructing square-law k-inflation from Planck data
• Non-canonical scalar field in low anisotropy universe with intermediate inflation
• Confronting the magnetically-induced holographic composite inflation with observation
• Inflationary Hubble Parameter from the Gravitational Wave Spectrum in the General Slow-roll Approximation
• Calculation of density fluctuation in inflationary epoch
• AliCPT Sensitivity to Cosmic Reheating
• Large-scale Structure from Quantum Fluctuations in the Early Universe
• Returning Back to Mukhanov Parametrization of Inflationary Equation of State
• Finite inflation in curved space
• Observational Viability of Anisotropic Inflation Revisited
• Chaotic inflation on the Randall-Sundrum 2-brane model
• Hamilton-Jacobi formalism for Generalized Chaplygin Gas models
• Quantum inflaton, primordial metric perturbations and CMB fluctuations
• Non-minimal kinetic coupled gravity: inflation on the Warped DGP brane
• Do We Live in a Vanilla Universe? Theoretical Perspectives on WMAP