Multipole decomposition of the general luminosity distance 'Hubble law' -- a new framework for observational cosmology

TL;DR

This paper introduces a multipole expansion framework for the luminosity distance-redshift relation in general space-times, enabling model-independent tests of cosmic anisotropy and the FLRW assumption.

Contribution

It develops a third-order series expansion of the luminosity distance incorporating multipole coefficients, allowing for a finite, interpretable set of anisotropic parameters.

Findings

Exact anisotropic Hubble law with 9, 25, 61 degrees of freedom at increasing orders.

Enables model-independent determination of local cosmic dynamics.

Provides a new framework for testing cosmological isotropy and the FLRW model.

Abstract

We present the luminosity distance series expansion to third order in redshift for a general space-time 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 Friedmann-Lema\^{\i}tre-Robertson-Walker (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.