Statistical isotropy violation of the CMB brightness fluctuations

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.083008· OSTI ID:21409555

Aich, Moumita; Souradeep, Tarun ^[1]

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1. Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007 (India)

Certain anomalies at large angular scales in the cosmic microwave background (CMB) measured by WMAP have been suggested as possible evidence of breakdown of statistical isotropy (SI). SI violation of cosmological perturbations is a generic feature of ultralarge scale structure of the cosmos and breakdown of global symmetries. Most CMB photons free-stream to the present from the surface of last scattering. It is thus reasonable to expect statistical isotropy violation in the CMB photon distribution observed now to have originated from SI violation in the baryon-photon fluid at last scattering, in addition to anisotropy of the primordial power spectrum studied earlier in the literature. We consider the generalized anisotropic brightness distribution fluctuations, {Delta}(k-vector, n-circumflex, {tau}) (at conformal time {tau}) in contrast to the SI case where it is simply a function of |k-vector| and k-circumflex{center_dot}n-circumflex. The brightness fluctuations expanded in bipolar spherical harmonic (BipoSH) series can then be written as {Delta}{sub l{sub 1}}{sub l{sub 2}}{sup LM}(k,{tau}), where L>0 terms encode deviations from statistical isotropy. Violation of SI encoded in the present off-diagonal elements of the harmonic space correlation <a{sub lm}a{sub l}{sup '}{sub m}{sup '}*>, equivalently, the BipoSH coefficients A{sub ll}{sup 'LM}, are then related to the generalized BipoSH brightness fluctuation terms at present. We study the evolution of {Delta}{sub l{sub 1}}{sub l{sub 2}}{sup LM}(k,{tau}) from nonzero terms {Delta}{sub l{sub 3}}{sub l{sub 4}}{sup LM}(k,{tau}{sub s}) at last scattering, in the free-streaming regime. We show that the terms with given BipoSH multipole LM evolve independently. Moreover, similar to the SI case, power at small spherical harmonic (SH) multipoles of {Delta}{sub l{sub 3}}{sub l{sub 4}}{sup LM}(k,{tau}{sub s}) at the last scattering is transferred to {Delta}{sub l{sub 1}}{sub l{sub 2}}{sup LM}(k,{tau}) at larger SH multipoles. The structural similarity is more apparent in the asymptotic expression for large values of the final SH multipoles. This formalism allows an elegant identification of any SI violation observed today to a possible origin in SI violating physics present in the baryon-photon fluid. This is illustrated for the known result of SI violating angular correlations due to the presence of a homogeneous magnetic field in the baryon-photon fluid.

• OSTI ID: 21409555
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.083008; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR CORRELATION
ANISOTROPY
ASYMPTOTIC SOLUTIONS
BARYONS
BRIGHTNESS
DISTRIBUTION
DISTURBANCES
FLUCTUATIONS
ISOTROPY
MAGNETIC FIELDS
PERTURBATION THEORY
PHOTONS
RELICT RADIATION
SCATTERING
SPACE
SPECTRA
SPHERICAL CONFIGURATION
SYMMETRY
UNIVERSE
BOSONS
CONFIGURATION
CORRELATIONS
ELECTROMAGNETIC RADIATION
ELEMENTARY PARTICLES
FERMIONS
HADRONS
MASSLESS PARTICLES
MATHEMATICAL SOLUTIONS
MICROWAVE RADIATION
OPTICAL PROPERTIES
PHYSICAL PROPERTIES
RADIATIONS
VARIATIONS