Harmonic expansion of the anisotropy of the 3K background radiation for arbitrary linear perturbations of the Friedmann cosmology

Astronomy and Astrophysics – Astrophysics

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Background Radiation, Cosmology, Relic Radiation, Anisotropy, Density Wave Model, Gravitational Waves, Perturbation Theory

Scientific paper

The author calculates the harmonic expansion of the anisotropy of the 3K cosmic background radiation for cosmological density, velocity and gravitational waves with scales exceeding the particle horizon at the last scattering redshift. He shows that each Lifshitz-Khalatnikov perturbative mode excites only one harmonic in the radiation anisotropy at most. Magnetic parity modes of velocity and gravitational waves give no anisotropy in the linear theory. For all of the remaining modes the author computes "conversion coefficients" which allow to derive quickly the harmonic amplitudes of the anisotropy from the corresponding multipole components of any arbitrary wavepacket. A few important examples of wavepacket are considered explicitly.

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