http://arxiv.org/abs/1908.10757
The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. This can be accomplished by introducing a tetrad at the observer point representing that frame. In this paper we consider the tetrad formalism of General Relativity and develop a new formalism for describing cosmological observables. It is based on the “observer space-time” manifold, whose coordinates are the proper time, redshift and angles an observer uses to parametrize measurements, and on which the rest of the observables are defined. This manifold does not have to be diffeomorphic to the true space-time and allows us to resolve caustics in the latter, in contrast with similar coordinate-based formalisms. We work out the definitions and equations for the angular diameter distance, weak lensing and number count observables. As for the ones associated to the CMB, they lie inside the phase space matrix distribution of the photon fluid evaluated at the observer point and pulled back on the observer sky. The second part of this paper is devoted to general-relativistic matrix kinetic theory. Here too the tetrad formalism appears as the natural approach for relating the macroscopic dynamics to the microscopic QFT. Part of the presented material is known and is included for completeness, but we provide more detailed discussions over some subtle issues and we also consider an alternative construction of the collision term which deviates from the standard one at higher order in the loop corrections. In summary, the present paper contains all the required structures for computations in cosmology with exact and model-independent cosmological observables. The associated linear perturbation theory will be given in a companion paper.
E. Mitsou and J. Yoo
Thu, 29 Aug 19
3/55
Comments: 108 pages
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