Generalized modelindependent characterization of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe
Abstract
We determine the cosmic expansion rate from supernovae of type Ia to set up a databased distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrization of a Friedmann cosmological model. The scale, determined by the Hubble constant H_{0}, is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio D is determined from the Pantheon sample. Inserting D and its uncertainty into the lensing equations for given H_{0}, especially the timedelay equation between a pair of multiple images, allows to determine lens properties, especially differences in the lensing potential (Δϕ), without specifying a cosmological model. We expand the luminosity distances into an analytic orthonormal basis, determine the maximumlikelihood weights for the basis functions by a globally optimal χ^{2}parameter estimation, and derive confidence bounds by Monte Carlo simulations. For typical strong lensing configurations between z = 0.5 and 1.0, Δϕ can be determined with a relative imprecision of 1.7 per cent, assuming imprecisions of the time delay and the redshift of the lens on the order of 1 per cent. With only a small, tolerable loss in precision, the modelindependent lens characterisation developed in this paper series can be generalised by dropping the specific Friedmann model to determine D in favour of a databased distance ratio. Moreover, for any astrophysical application, the approach presented here, provides distance measures for z ≤ 2.3 that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 2019
 DOI:
 10.1093/mnras/stz2717
 arXiv:
 arXiv:1812.04002
 Bibcode:
 2019MNRAS.490.1913W
 Keywords:

 gravitational lensing: strong;
 gravitational lensing: weak;
 methods: analytical;
 supernovae: general;
 distance scale;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 16 pages, 4 figures, accepted for publication in MNRAS, comments welcome