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The anisotropies of the cosmic microwave background (CMB) are computed for the half-turn space E_2 which represents a compact flat model of the Universe, i.e. one with finite volume. This model is inhomogeneous in the sense that the…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-20 R. Aurich , S. Lustig

We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects…

Analysis of PDEs · Mathematics 2022-09-29 Tracey Balehowsky , Antti Kujanpää , Matti Lassas , Tony Liimatainen

We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…

Numerical Analysis · Mathematics 2021-01-12 Thuy T. Le , Loc H. Nguyen , Thi-Phong Nguyen , William Powell

We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation is measured on an arc. The attenuation and scattering…

Analysis of PDEs · Mathematics 2021-11-17 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

In this article, for a fourth-order parabolic equation which is closely related for example to the Cahn-Hilliard equation, we study an inverse source problem by interior data and the continuation of solution from lateral Cauchy data. Our…

Analysis of PDEs · Mathematics 2020-09-25 O. Yu. Imanuvilov , M. Yamamoto

The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…

Analysis of PDEs · Mathematics 2021-12-03 Mourad Sini , Haibing Wang

Cosmic microwave background (CMB) anisotropy is our richest source of cosmological information; the standard cosmological model was largely established thanks to study of the temperature anisotropies. By the end of the decade, the Planck…

Astrophysics · Physics 2009-11-11 James G. Bartlett

We question the global universe isotropy by probing the alignment of local structures in the cosmic microwave background (CMB) radiation. The original method proposed relies on a steerable wavelet decomposition of the CMB signal on the…

Astrophysics · Physics 2007-05-23 Y. Wiaux , P. Vielva , E. Martinez-Gonzalez , P. Vandergheynst

The analysis of anisotropies in the cosmic microwave background (CMB) has become an extremely valuable tool for cosmology. We even have hopes that planned CMB anisotropy experiments may revolutionize cosmology. Together with determinations…

Astrophysics · Physics 2011-04-15 Ruth Durrer

Accurate measurements of the cosmic microwave background (CMB) anisotropies with an angular resolution of a few arcminutes can be used to determine fundamental cosmological parameters such as the densities of baryons, cold and hot dark…

Astrophysics · Physics 2016-01-13 J. Richard Bond , George Efstathiou , Max Tegmark

This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of…

Probability · Mathematics 2018-03-01 Samuel Punshon-Smith , Scott Smith

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

The Planck mission has conclusively detected lensing of the Cosmic Microwave Background (CMB) radiation from foreground sources to an overall significance of greater than $25\sigma$. The high precision of this measurement motivates the…

Cosmology and Nongalactic Astrophysics · Physics 2014-06-25 S. -C. Su , Eugene A. Lim

We review the theory of the temperature anisotropy and polarization of the cosmic microwave background (CMB) radiation, and describe what we have learned from current CMB observations. In particular, we discuss how the CMB is being used to…

Cosmology and Nongalactic Astrophysics · Physics 2010-02-22 Anthony Challinor , Hiranya Peiris

We present a 1+3 covariant discussion of the contribution of gravitational waves to the anisotropy of the CMB in an almost-Friedmann-Robertson-Walker universe. Our discussion is based in the covariant approach to perturbations in cosmology,…

Astrophysics · Physics 2014-10-13 Anthony Challinor

The Cosmic Microwave Background (CMB) is a relict of the early universe. Its perfect 2.725K blackbody spectrum demonstrates that the universe underwent a hot, ionized early phase; its anisotropy (about 80 \mu K rms) provides strong evidence…

Instrumentation and Methods for Astrophysics · Physics 2015-06-11 Paolo de Bernardis , Silvia Masi

We consider how microlocal methods developed for tomographic problems can be used to detect singularities of the Lorentzian metric of the Universe using measurements of the Cosmic Microwave Background radiation. The physical model we study…

Mathematical Physics · Physics 2015-05-13 Matti Lassas , Lauri Oksanen , Plamen Stefanov , Gunther Uhlmann

The Cosmic Microwave Background (CMB) encodes information on the origin and evolution of the universe, buried in a fractional anisotropy of one part in 100,000 on angular scales from arcminutes to tens of degrees. We await the coming…

Astrophysics · Physics 2007-05-23 J. Richard Bond , Robert G. Crittenden , Andrew H. Jaffe , Lloyd Knox

In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's…

Cosmology and Nongalactic Astrophysics · Physics 2014-10-23 Ryo Saito , Atsushi Naruko , Takashi Hiramatsu , Misao Sasaki

Spectral distortions of the Cosmic Microwave Background (CMB) offer the possibility of probing processes which occurred during the evolution of our Universe going back up to Z$\simeq 10^7$. Unfortunately all the attempts so far carried out…

Instrumentation and Methods for Astrophysics · Physics 2017-02-22 Giorgio Sironi