Strongly lensed supernovae as a self-sufficient probe of the distance duality relation
Physics of the Dark Universe
The observation of strongly lensed Type Ia supernovae enables both the luminosity and angular diameter distance to a source to be measured simultaneously using a single observation. This feature can be used to measure the distance duality parameter η(z) without relying on multiple datasets and cosmological assumptions to reconstruct the relation between angular and luminosity distances. In this paper, we show how this can be achieved by future observations of strongly lensed Type Ia systems.
... ng simulated datasets, we reconstruct the function η(z) using both parametric and non-parametric approaches, focusing on Genetic Algorithms and Gaussian processes for the latter. In the parametric approach, we find that in the realistic scenario of N lens = 20 observed systems, the parameter ϵ 0 used to describe the trend of η(z) can be constrained with the precision achieved by current SNIa and BAO surveys, while in the futuristic case (N lens = 1000) these observations could be competitive with the forecast precision of upcoming LSS and SN surveys. Using the machine learning approaches of Genetic Algorithms and Gaussian processes, we find that both reconstruction methods are generally well able to correctly recover the underlying fiducial model in the mock data, even in the realistic case of N lens = 20. Both approaches learn effectively from the features of the mock data points, yielding 1σ constraints that are in excellent agreement with the parameterised results. (F. Renzi). used as a tracer of the distance-redshift relation, and to infer constraints on cosmological parameters [6-9]. While lensing can happen at all scales (i.e. the lens can be as small as a star or as big as a galaxy cluster), for cosmological inference one typically relies on galaxy-galaxy lensing events . This is because galaxies are believed to have simple mass profiles that can be effectively parameterised as a power law, and a larger lensing probability, making them more abundant in the sky, although it has been shown that uncertainties in the mass profiles play a significant role in constraining cosmological parameters  . Furthermore, by combining measurements of the velocity dispersion of the stars orbiting the lensing galaxy with the strong lensing time delay, it is possible to obtain a measurement of the angular diameter distance to the lens, which breaks the degeneracy between different lens mass profiles     . However, strong lensing observables are significantly affected by the specific alignment between the lens and the source, making only a fraction of the observed lensing events suitable for the extraction of cosmological information [15, 16] . To achieve percentage accuracy on time delay measurements, the image separation is required to be > 1 ′′ , the magnitude of the faintest image m i < 21 in the i-band, and the lensing galaxy magnitude m i < 22  . Therefore, it is clear that, along with