Generalised model-independent characterisation of strong gravitational lenses V: lensing distance ratio in a general Friedmann universe. (arXiv:1812.04002v1 [astro-ph.CO])

Generalised model-independent characterisation of strong gravitational lenses V: lensing distance ratio in a general Friedmann universe. (arXiv:1812.04002v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Wagner_J/0/1/0/all/0/1">Jenny Wagner</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Meyer_S/0/1/0/all/0/1">Sven Meyer</a>

Determining the cosmic expansion history from a sample of supernovae of type
Ia, data-based cosmic distance measures can be set up that make no assumptions
about the constituents of the universe, i.e. about a specific cosmological
model. The overall scale, usually determined by the Hubble constant $H_0$, is
the only free parameter left. We investigate to which accuracy and precision
the lensing distance ratio D of our distance to the lens, to the source, and
their relative distance can be determined from the most recent Pantheon sample.
Subsequently inserting D and its uncertainty into the gravitational lensing
equations for given $H_0$, esp. the time-delay equation between a pair of
multiple images, allows to determine lens properties, esp. differences in the
lensing potential (Delta Phi), without specifying a cosmological model.
Alternatively, given Delta Phi$,$ between multiple images, e.g. by a lens
model, $H_0$ can be determined. For typical strong gravitational lensing
configurations between z=0.5 and z=1.0, we find that Delta Phi$,$ can be
determined with a relative imprecision of 1.7%, assuming imprecisions of the
time delay and the redshift of the lens on the order of 1%. Using a
$Lambda$CDM model, the relative imprecision of Delta Phi$,$ is 1.4%.
Minimum relative imprecisions for $H_0$ amount to 20% and 10% for galaxy- and
galaxy-cluster-scale lenses when including measurements of velocity dispersions
in a single-lens-plane model. With only a small, tolerable loss in precision,
the model-independent lens characterisation developed in this paper series can
be generalised by dropping the specific Friedmann model to determine D in
favour of a data-based distance ratio. For any astrophysical application, the
approach presented here, provides distance measures up to z=2.3 that are valid
in any homogeneous, isotropic universe with general relativity as theory of
gravity.

Determining the cosmic expansion history from a sample of supernovae of type
Ia, data-based cosmic distance measures can be set up that make no assumptions
about the constituents of the universe, i.e. about a specific cosmological
model. The overall scale, usually determined by the Hubble constant $H_0$, is
the only free parameter left. We investigate to which accuracy and precision
the lensing distance ratio D of our distance to the lens, to the source, and
their relative distance can be determined from the most recent Pantheon sample.
Subsequently inserting D and its uncertainty into the gravitational lensing
equations for given $H_0$, esp. the time-delay equation between a pair of
multiple images, allows to determine lens properties, esp. differences in the
lensing potential (Delta Phi), without specifying a cosmological model.
Alternatively, given Delta Phi$,$ between multiple images, e.g. by a lens
model, $H_0$ can be determined. For typical strong gravitational lensing
configurations between z=0.5 and z=1.0, we find that Delta Phi$,$ can be
determined with a relative imprecision of 1.7%, assuming imprecisions of the
time delay and the redshift of the lens on the order of 1%. Using a
$Lambda$CDM model, the relative imprecision of Delta Phi$,$ is 1.4%.
Minimum relative imprecisions for $H_0$ amount to 20% and 10% for galaxy- and
galaxy-cluster-scale lenses when including measurements of velocity dispersions
in a single-lens-plane model. With only a small, tolerable loss in precision,
the model-independent lens characterisation developed in this paper series can
be generalised by dropping the specific Friedmann model to determine D in
favour of a data-based distance ratio. For any astrophysical application, the
approach presented here, provides distance measures up to z=2.3 that are valid
in any homogeneous, isotropic universe with general relativity as theory of
gravity.

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