Constraining Inflation

Abstract

Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of inflationary dynamics. It automatically includes information from sub-leading terms in slow roll, and facilitatesthe inclusion of priors based on the duration on inflation. We show that at low inflationary scales the Hamilton-Jacobi equations simplify considerably. We provide a new classification scheme for inflationary models, based solely on the number of parameters needed to specify the potential, and provide forecasts for likely bounds on the slow roll parameters from future datasets. A minimal running of the spectral index, induced solely by the first two slow roll parameters (εand η) appears to be effectively undetectable by realistic Cosmic Microwave Background experiments. However, we show that the ability to detect this signal increases with the lever arm in comoving wavenumber, and we conjecture that high redshift 21 cm data may allow tests of second order consistency conditions on inflation. Finally, we point out that the second order corrections to the spectral index are correlated with the inflationary scale, and thus the amplitude of the CMB B-mode.

32 pages. v3

References in corpus (61)

• Efficient Computation of CMB anisotropies in closed FRW models
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Hybrid Inflation
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• An All-Sky Analysis of Polarization in the Microwave Background
• False Vacuum Inflation with Einstein Gravity
• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Reconstructing the Inflaton Potential --- an Overview
• The 2dF Galaxy Redshift Survey: The power spectrum and the matter content of the universe
• What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?
• Cosmic Microwave Background Anisotropies
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• How long before the end of inflation were observable perturbations produced?
• Gravitational Lensing Effect on Cosmic Microwave Background Polarization
• Cosmological Parameter Estimation Using 21 cm Radiation from the Epoch of Reionization
• Cosmological-Parameter Determination with Microwave Background Maps
• String Cosmology: A Review
• Inflationary perturbations from a potential with a step
• Cosmic Complementarity: Joint Parameter Estimation from CMB Experiments and Redshift Surveys
• A limit on the detectability of the energy scale of inflation
• How accurately can 21 cm tomography constrain cosmology?
• CBR Anisotropy and the Running of the Scalar Spectral Index
• Cosmological parameter estimation and the inflationary cosmology
• The Density Perturbation Power Spectrum to Second-Order Corrections in the Slow-Roll Expansion
• Inflation: flow, fixed points and observables to arbitrary order in slow roll
• Inflation model constraints from the Wilkinson Microwave Anisotropy Probe three-year data
• Reconstructing the Inflaton Potential---in Principle and in Practice
• Kinematic Constraints to the Key Inflationary Observables
• Constraining slow-roll inflation with WMAP and 2dF
• Considerations in optimizing CMB polarization experiments to constrain inflationary physics
• Measuring Cosmological Parameters with Cosmic Microwave Background Experiments
• Second Order General Slow-Roll Power Spectrum
• Cosmology in the Next Millennium: Combining MAP and SDSS Data to Constrain Inflationary Models
• Multiple Inflation, Cosmic String Networks and the String Landscape
• Observing the Inflaton Potential
• Constraining Inflation with Cosmic Microwave Background Polarization
• Recovering the Inflationary Potential and Primordial Power Spectrum With a Slow Roll Prior: Methodology and Application to WMAP 3 Year Data
• Inflationary predictions for scalar and tensor fluctuations reconsidered
• Monte Carlo reconstruction of the inflationary potential
• On the inflationary flow equations
• Slow Roll Reconstruction: Constraints on Inflation from the 3 Year WMAP Dataset
• Reconstructing the Inflaton Potential---Perturbative Reconstruction to Second Order
• Recovering the Inflationary Potential
• The exact numerical treatment of inflationary models
• Detectability of Tensor Perturbations Through CBR Anisotropy (final published version)
• Second-Order Reconstruction of the Inflationary Potential
• Inflationary Cosmology Connecting Dark Energy and Dark Matter
• Inflationary Potential Reconstruction for a WMAP Running Power Spectrum
• The Lyth Bound and the End of Inflation
• Deciphering Inflation with Gravitational Waves: Cosmic Microwave Background Polarization vs. Direct Detection with Laser Interferometers
• How robust are inflation model and dark matter constraints from cosmological data?
• Theoretical Uncertainties in Inflationary Predictions
• Running Spectral Index as a Probe of Physics at High Scales
• Microwave background constraints on inflationary parameters
• Limits on primordial power spectrum resolution: An inflationary flow analysis
• Dynamics of the Inflationary Flow Equations
• Clover - A B-mode polarization experiment
• How to constrain inflationary parameter space with minimal priors
• From the production of primordial perturbations to the end of inflation
• On bounded solutions for second order linear differential equations with negative stiffness

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• Bayesian Analysis of Inflation: Parameter Estimation for Single Field Models
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• The Knotted Sky II: Does BICEP2 require a nontrivial primordial power spectrum?
• Constraining inflation with future galaxy redshift surveys
• Bayesian Analysis of Inflation III: Slow Roll Reconstruction Using Model Selection
• Ultracompact minihalos as probes of inflationary cosmology
• Cosmological parameters after WMAP5: forecasts for Planck and future galaxy surveys
• Single-field inflation constraints from CMB and SDSS data
• Gravitational Collapse in the Post-Inflationary Universe
• Observational constraints on K-inflation models
• Gravity Waves and Primordial Black Holes in Scalar Warm Little Inflation
• Cosmological constraints on general, single field inflation
• Constraining the kinetically dominated Universe
• Formation of inflaton halos after inflation
• Approach to exact inflation in modified Friedmann equation
• Inflationary Potential from 21 cm Tomography and Planck
• Forecasting Chemical Abundance Precision for Extragalactic Stellar Archaeology
• Running primordial perturbations: Inflationary Dynamics and Observational Constraints
• Constraining Cosmic Inflation with Observations: Prospects for 2030
• Signatures of the Very Early Universe: Inflation, Spatial Curvature and Large Scale Anomalies
• Non-Gaussian Shape Recognition
• Non-Gaussian signatures of general inflationary trajectories
• Expectations for Inflationary Observables: Simple or Natural?
• Probing the primordial power spectra with inflationary priors
• Obtaining a scalar fifth force via a broken-symmetry couple between the scalar field and matter
• Updated constraints on the primordial power spectrum at sub-Mpc scales
• From WMAP to Planck: Exact reconstruction of 4- and 5-dimensional inflationary potential from high precision CMB measurements
• Non-Gaussianity in D3-brane inflation