Strongly lensed supernovae as a self-sufficient probe of the distance duality relation

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. Using 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 parameterε0used 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.