Information field theory for cosmological perturbation reconstruction and non-linear signal analysis

Abstract

We develop information field theory (IFT) as a means of Bayesian inference on spatially distributed signals, the information fields. A didactical approach is attempted. Starting from general considerations on the nature of measurements, signals, noise, and their relation to a physical reality, we derive the information Hamiltonian, the source field, propagator, and interaction terms. Free IFT reproduces the well known Wiener-filter theory. Interacting IFT can be diagrammatically expanded, for which we provide the Feynman rules in position-, Fourier-, and spherical harmonics space, and the Boltzmann-Shannon information measure. The theory should be applicable in many fields. However, here, two cosmological signal recovery problems are discussed in their IFT-formulation. 1) Reconstruction of the cosmic large-scale structure matter distribution from discrete galaxy counts in incomplete galaxy surveys within a simple model of galaxy formation. We show that a Gaussian signal, which should resemble the initial density perturbations of the Universe, observed with a strongly non-linear, incomplete and Poissonian-noise affected response, as the processes of structure and galaxy formation and observations provide, can be reconstructed thanks to the virtue of a response-renormalization flow equation. 2) We design a filter to detect local non-linearities in the cosmic microwave background, which are predicted from some Early-Universe inflationary scenarios, and expected due to measurement imperfections. This filter is the optimal Bayes' estimator up to linear order in the non-linearity parameter and can be used even to construct sky maps of non-linearities in the data.

38 pages, 6 figures, LaTeX; version accepted by PRD

References in corpus (25)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Bayes in the sky: Bayesian inference and model selection in cosmology
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectra
• Detection of primordial non-Gaussianity (fNL) in the WMAP 3-year data at above 99.5% confidence
• The shape of primordial non-Gaussianity and the CMB bispectrum
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Perturbation Theory Reloaded: Analytical Calculation of Non-linearity in Baryonic Oscillations in the Real Space Matter Power Spectrum
• Resumming Cosmic Perturbations
• Reconstructed Density and Velocity Fields from the 2MASS Redshift Survey
• Clustering of dark matter tracers: renormalizing the bias parameters
• Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function
• Rejuvenating the matter power spectrum: restoring information with a logarithmic density mapping
• Dark matter clustering: a simple renormalization group approach
• Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
• Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background
• Perturbation Theory Reloaded II: Non-linear Bias, Baryon Acoustic Oscillations and Millennium Simulation In Real Space
• Estimation of Polarized Power Spectra by Gibbs sampling
• Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background II: Partial Sky Coverage and Inhomogeneous Noise
• Baryonic Acoustic Oscillations via the Renormalization Group
• Using the Zeldovich dynamics to test expansion schemes
• Expansion schemes for gravitational clustering: computing two-point and three-point functions
• Optimal Image Reconstruction in Radio Interferometry
• On the Large-Scale Structure of the Universe as given by the Voronoi Diagrams
• Scaling Laws in the Cosmic Structure and Renormalization Group

Cited by in corpus (92)

• An improved map of the Galactic Faraday sky
• Estimating extragalactic Faraday rotation
• Local Gravity versus Local Velocity: Solutions for $\beta$ and nonlinear bias
• Fast Hamiltonian sampling for large scale structure inference
• Gravitational redshift and other redshift-space distortions of the imaginary part of the power spectrum
• Reconstruction of Gaussian and log-normal fields with spectral smoothness
• Bayesian non-linear large scale structure inference of the Sloan Digital Sky Survey data release 7
• On the Three-Dimensional Structure of Local Molecular Clouds
• NIFTY - Numerical Information Field Theory - a versatile Python library for signal inference
• Primordial Non-Gaussianity in the Cosmic Microwave Background
• Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methods
• IMAGINE: A comprehensive view of the interstellar medium, Galactic magnetic fields and cosmic rays
• The Denoised, Deconvolved, and Decomposed Fermi $\gamma$-ray sky - An application of the D${}^3$PO algorithm
• Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
• RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy
• The Galactic Faraday depth sky revisited
• Information theory for fields
• Inference with minimal Gibbs free energy in information field theory
• The axis of evil - a polarization perspective
• Comparison of classical and Bayesian imaging in radio interferometry
• Unified Radio Interferometric Calibration and Imaging with Joint Uncertainty Quantification
• SIBELIUS-DARK: a galaxy catalogue of the Local Volume from a constrained realisation simulation
• Galactic dark matter search via phenomenological astrophysics modeling
• Constraining Magnetic Fields in the Circumgalactic Medium
• Consistency tests of field level inference with the EFT likelihood
• D${}^3$PO - Denoising, Deconvolving, and Decomposing Photon Observations
• Using rotation measure grids to detect cosmological magnetic fields -- a Bayesian approach
• Faraday synthesis: The synergy of aperture and rotation measure synthesis
• A compiled catalog of rotation measures of radio point sources
• Learning Curves for Deep Neural Networks: A Gaussian Field Theory Perspective
• The VIMOS Public Extragalactic Redshift Survey (VIPERS): Reconstruction of the redshift-space galaxy density field
• Reconstructing signals from noisy data with unknown signal and noise covariance
• A fast semi-discrete optimal transport algorithm for a unique reconstruction of the early Universe
• Density estimation on small datasets
• A new approach to multi-frequency synthesis in radio interferometry
• Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior
• Rapid and deterministic estimation of probability densities using scale-free field theories
• Spatially Coherent 3D Distributions of HI and CO in the Milky Way
• Local non-Gaussianity in the Cosmic Microwave Background the Bayesian way
• Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation
• Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification
• Unification of field theory and maximum entropy methods for learning probability densities
• Information field dynamics for simulation scheme construction
• Bayesian field theoretic reconstruction of bond potential and bond mobility in single molecule force spectroscopy
• Generic inference of inflation models by non-Gaussianity and primordial power spectrum reconstruction
• Improving stochastic estimates with inference methods: calculating matrix diagonals
• On the complexity and the information content of cosmic structures
• Cosmic expansion history from SNe Ia data via information field theory -- the charm code
• A Reputation Game Simulation: Emergent Social Phenomena from Information Theory
• Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
• Tomography of the Galactic free electron density with the Square Kilometer Array
• Denoising, deconvolving and decomposing multi-domain photon observations- The D4PO algorithm
• Causal, Bayesian, & Non-parametric Modeling of the SARS-CoV-2 Viral Load Distribution vs. Patient's Age
• Information Field Theory and Artificial Intelligence
• A Bayesian method for pulsar template generation
• A method for reconstructing the Galactic magnetic field using dispersion of fast radio bursts and Faraday rotation of radio galaxies
• Noisy independent component analysis of auto-correlated components
• Multi-Component Imaging of the Fermi Gamma-ray Sky in the Spatio-spectral Domain
• An improved estimator for non-Gaussianity in cosmic microwave background observations
• A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation
• Field dynamics inference via spectral density estimation
• Higher-Order Gravitational Lensing Reconstruction using Feynman Diagrams
• An Information Theoretic Exploration of Constrained MSSM
• Dynamic system classifier
• How complex is the cosmic web?
• Towards information optimal simulation of partial differential equations
• Improving self-calibration
• Consistency and convergence of simulation schemes in Information field dynamics
• Fast and precise way to calculate the posterior for the local non-Gaussianity parameter $f_{\text{nl}}$ from cosmic microwave background observations
• A probabilistic approach to phase calibration: I. Effects of source structure on fringe-fitting
• Operator Calculus for Information Field Theory
• Bayesian analysis of spatially distorted cosmic signals from Poissonian data
• Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars
• Sharpening up Galactic all-sky maps with complementary data - A machine learning approach
• A Bayesian Model for Bivariate Causal Inference
• Signal inference with unknown response: Calibration-uncertainty renormalized estimator
• D2O - a distributed data object for parallel high-performance computing in Python
• All-sky reconstruction of the primordial scalar potential from WMAP temperature data
• Renormalization group computation of likelihood functions for cosmological data sets
• Exploring the MeV Sky with a Combined Coded Mask and Compton Telescope: The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO)
• A dense dark matter core of the subhalo in the strong lensing system JVAS B1938+666
• Improved renormalization group computation of likelihood functions for cosmological data sets
• Enhancing Compton telescope imaging with maximum a posteriori estimation: a modified Richardson-Lucy algorithm for the Compton Spectrometer and Imager
• Non-parametric Bayesian reconstruction of Galactic magnetic fields using Information Field Theory: The inclusion of line-of-sight information in ultra-high energy cosmic ray backtracking
• Quantifying imperfect cognition via achieved information gain
• Latent-space Field Tension for Astrophysical Component Detection An application to X-ray imaging
• Bayesian parameter estimation of miss-specified models
• Bayesian Multi-wavelength Imaging of the LMC SN1987A with SRG/eROSITA
• The influence of the 3D Galactic gas structure on cosmic-ray transport and $\gamma$-ray emission
• Generic inference of inflation models by local non-Gaussianity
• A Bayesian Method for Air-Shower Reconstruction using Information Field Theory
• Dynamical field inference and supersymmetry