Monte Carlo reconstruction of the inflationary potential

Abstract

We present Monte Carlo reconstruction, a new method for ``inverting'' observational data to constrain the form of the scalar field potential responsible for inflation. This stochastic technique is based on the flow equation formalism and has distinct advantages over reconstruction methods based on a Taylor expansion of the potential. The primary ansatz required for Monte Carlo reconstruction is simply that inflation is driven by a single scalar field. We also require a very mild slow roll constraint, which can be made arbitrarily weak since Monte Carlo reconstruction is implemented at arbitrary order in the slow roll expansion. While our method cannot evade fundamental limits on the accuracy of reconstruction, it can be simply and consistently applied to poor data sets, and it takes advantage of the attractor properties of single-field inflation models to constrain the potential outside the small region directly probed by observations. We show examples of Monte Carlo reconstruction for data sets similar to that expected from the Planck satellite, and for a hypothetical measurement with a factor of five better parameter discrimination than Planck.

arXiv comment10 pages, 5 figures (RevTeX 4) Version submitted to PRD: references added, minor clarifications

References in corpus (20)

• Hybrid Inflation
• False Vacuum Inflation with Einstein Gravity
• Reconstructing the Inflaton Potential --- an Overview
• Formalising the Slow-Roll Approximation in Inflation
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• Inflationary perturbations from a potential with a step
• Higher order corrections to primordial spectra from cosmological inflation
• Inflation: flow, fixed points and observables to arbitrary order in slow roll
• Cosmic microwave background measurements can discriminate among inflation models
• Kinematic Constraints to the Key Inflationary Observables
• Observing the Inflaton Potential
• Constraining Inflation with Cosmic Microwave Background Polarization
• On the Problem of Predicting Inflationary Perturbations
• The Inflationary Perturbation Spectrum
• Second-Order Reconstruction of the Inflationary Potential
• The COBE Normalization for Standard CDM
• COBE-DMR-normalisation for inflationary flat dark matter models
• Inflaton potential reconstruction without slow-roll
• On the Stewart-Lyth Inverse Problem
• Stewart-Lyth Inverse Problem

Cited by in corpus (71)

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• Inflation and the Scale Dependent Spectral Index: Prospects and Strategies
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• Prospects for direct detection of primordial gravitational waves
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• Phenomenology of D-Brane Inflation with General Speed of Sound
• Bayesian Analysis of Inflation: Parameter Estimation for Single Field Models
• WMAPping inflationary physics
• Relic gravitational waves and their detection
• Recovering the Inflationary Potential and Primordial Power Spectrum With a Slow Roll Prior: Methodology and Application to WMAP 3 Year Data
• Cosmology From Random Multifield Potentials
• Dynamical behavior of generic quintessence potentials: constraints on key dark energy observables
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• Slow Roll Reconstruction: Constraints on Inflation from the 3 Year WMAP Dataset
• Implications of a Running Spectral Index for Slow Roll Inflation
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• MCMC analysis of WMAP3 and SDSS data points to broken symmetry inflaton potentials and provides a lower bound on the tensor to scalar ratio
• Implications of the Curvaton on Inflationary Cosmology
• Characterizing Inflationary Perturbations: The Uniform Approximation
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• Primordial Black Holes, Eternal Inflation, and the Inflationary Parameter Space after WMAP5
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• Constraining inflation with future galaxy redshift surveys
• The Lyth Bound and the End of Inflation
• Deciphering Inflation with Gravitational Waves: Cosmic Microwave Background Polarization vs. Direct Detection with Laser Interferometers
• Bayesian Analysis of Inflation III: Slow Roll Reconstruction Using Model Selection
• The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis
• Precision of Inflaton Potential Reconstruction from CMB Using the General Slow-Roll Approximation
• Towards a reliable calculation of relic radiation from primordial gravitational waves
• Limits on primordial power spectrum resolution: An inflationary flow analysis
• Constraining Inflation
• Horizon-Flow off-track for Inflation
• Cosmological constraints on general, single field inflation
• Dynamics of the Inflationary Flow Equations
• WMAP-normalized Inflationary Model Predictions and the Search for Primordial Gravitational Waves with Direct Detection Experiments
• Approach to exact inflation in modified Friedmann equation
• Observational Signatures of Gravitational Couplings in DBI Inflation
• The Polarization of the Cosmic Microwave Background Due to Primordial Gravitational Waves
• The Hubble Slow Roll Expansion for Multi Field Inflation
• Stochastic approaches to inflation model building
• Relations between canonical and non-canonical inflation
• How to constrain inflationary parameter space with minimal priors
• Optimizing future experimental probes of inflation
• Inflationary Potential from 21 cm Tomography and Planck
• Reconstructing large running-index inflaton potentials
• Phenomenological approaches of inflation and their equivalence
• Impact of general reionization scenarios on extraction of inflationary parameters
• From the production of primordial perturbations to the end of inflation
• The Degeneracy Problem in Non-Canonical Inflation
• Minimal Noncanonical Cosmologies
• Let Effective Field Theory of Inflation flow: stochastic generation of models with red/blue tensor tilt
• New Solutions of the Inflationary Flow Equations
• Identifying the inflaton with primordial gravitational waves
• Probing the era of reheating for reconstructed inflationary potential in the RS II braneworld
• The History of Inflation from Microwave Background Polarimetry and Laser Interferometry
• Non-Gaussian signatures of general inflationary trajectories
• Probing the primordial power spectra with inflationary priors
• Braneworld inflation from an effective field theory after WMAP three-year data
• Old Dark Energy
• Troubles for observing the inflaton potential
• Understanding selection effects in observed samples of cataclysmic variables
• Inflation after WMAP3
• Gravitational Wave Direct Detection does not Constrain the Tensor Spectral Index at CMB Scales
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• Planck and WMAP constraints on generalised Hubble flow inflationary trajectories
• From WMAP to Planck: Exact reconstruction of 4- and 5-dimensional inflationary potential from high precision CMB measurements
• Softly Fine-Tuned Standard Model and the Scale of Inflation
• Do We Live in a Vanilla Universe? Theoretical Perspectives on WMAP