arXiv · 0706.1767
We review the current status, and some open issues, of VHE astrophysics.
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Massimo Persic, Alessandro De Angelis. 2007-06-12. VHE astrophysics: recent developments. https://arxiv.org/abs/0706.1767
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The exact 1+3 covariant multipole hierarchy for the CMB brightness contains kinematic couplings between the shear, acceleration and vorticity of the observers and the temperature multipoles, whose coefficients grow linearly in $\ell$. They are products of first-order quantities, so linearization about FLRW removes them. Here they are kept as sources in a weakly nonlinear extension of the almost-FLRW temperature anisotropies, and evaluated in the aligned-wavevector, weak-coupling limit. In the Newtonian frame the acceleration terms cancel at leading order in $1/\ell$. In the total (CDM) frame the shear terms cancel in the same way, to a residual of about $3/\ell$ of either term. Earlier versions of this paper reported that the total-frame terms do not cancel, and inferred a mildly nonlinear Rees-Sciama imprint near $\ell \sim 100 - 300$. That result came from a sign misprint in the $\ell-2$ shear coupling and is withdrawn; see the Note added. The $O(\ell)$ couplings are the multipole form of gravitational lensing and observer aberration, both already in the standard treatment. The explicit kinematic couplings written here are only part of the full second-order propagation source; the perturbed free-streaming contribution is linearized away in this paper.
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