Multipole decomposition of the general luminosity distance ‘Hubble law’ — a new framework for observational cosmology. (arXiv:2010.06534v2 [astro-ph.CO] UPDATED)

Multipole decomposition of the general luminosity distance ‘Hubble law’ — a new framework for observational cosmology. (arXiv:2010.06534v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Heinesen_A/0/1/0/all/0/1">Asta Heinesen</a>

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.

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.

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