Multipole decomposition of the general luminosity distance 'Hubble law'  a new framework for observational cosmology
Abstract
We present the luminosity distance series expansion to third order in redshift for a general spacetime with no assumption on the metric tensor or the field equations prescribing it. It turns out that the coefficients of this general 'Hubble law' can be expressed in terms of a finite number of physically interpretable multipole coefficients. The multipole terms can be combined into effective direction dependent parameters replacing the Hubble constant, deceleration parameter, curvature parameter, and 'jerk' parameter of the FriedmannLemaîtreRobertsonWalker (FLRW) class of metrics. Due to the finite number of multipole coefficients, the exact anisotropic Hubble law is given by 9, 25, 61 degrees of freedom in the $\mathcal{O}(z)$, $\mathcal{O}(z^2)$, $\mathcal{O}(z^3)$ vicinity of the observer respectively, where $z\!:=\,$redshift. This makes possible model independent determination of dynamical degrees of freedom of the cosmic neighbourhood of the observer and direct testing of the FLRW ansatz. We argue that the derived multipole representation of the general Hubble law provides a new framework with broad applications in observational cosmology.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.06534
 Bibcode:
 2020arXiv201006534H
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 22 pages, v2: small additions, typos corrected, references added, matches published version in JCAP