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 be measured simultaneously using single observation. This feature can used measure duality parameter $\eta(z)$ without relying on multiple datasets cosmological assumptions reconstruct relation between distances. In this paper, we show how achieved by future observations systems. Using simulated datasets, function parametric non-parametric approaches, focusing Genetic Algorithms Gaussian processes for latter. approach, find that in realistic scenario $N_{\rm lens}=20$ observed systems, $\epsilon_0$ describe trend constrained with precision current SNIa BAO surveys, while futuristic case ($N_{\rm lens}=1000$) these could competitive forecast upcoming LSS SN surveys. machine learning approaches processes, reconstruction methods are generally well able correctly recover underlying fiducial model mock data, even lens}=20$. Both learn effectively from features data points, yielding $1\sigma$ constraints excellent agreement parameterised results.