Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis
- Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Strasse 1, 85741 Garching (Germany)
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 nonlinear, 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 nonlinearities 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 nonlinearity parameter and can be used even to construct sky maps of nonlinearities in the data.
- OSTI ID:
- 21313395
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 10; Other Information: DOI: 10.1103/PhysRevD.80.105005; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
DENSITY
DISTRIBUTION
DISTURBANCES
EQUATIONS
FIELD THEORIES
GALAXIES
HAMILTONIANS
INTERACTIONS
NOISE
NONLINEAR PROBLEMS
PERTURBATION THEORY
PROPAGATOR
QUANTUM FIELD THEORY
RELICT RADIATION
RENORMALIZATION
SPACE
SPHERICAL HARMONICS
UNIVERSE