Strongly lensed supernovae as a self-sufficient probe of the distance duality relation. (arXiv:2010.04155v2 [astro-ph.CO] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Renzi_F/0/1/0/all/0/1">Fabrizio Renzi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hogg_N/0/1/0/all/0/1">Natalie B. Hogg</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Martinelli_M/0/1/0/all/0/1">Matteo Martinelli</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Nesseris_S/0/1/0/all/0/1">Savvas Nesseris</a>

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 $eta(z)$ 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 $eta(z)$ 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

$N_{rm lens}=20$ observed systems, the parameter $epsilon_0$ used to describe

the trend of $eta(z)$ can be constrained with the precision achieved by

current SNIa and BAO surveys, while in the futuristic case ($N_{rm

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 $N_{rm lens}=20$. Both

approaches learn effectively from the features of the mock data points,

yielding $1sigma$ constraints that are in excellent agreement with the

parameterised results.

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 $eta(z)$ 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 $eta(z)$ 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

$N_{rm lens}=20$ observed systems, the parameter $epsilon_0$ used to describe

the trend of $eta(z)$ can be constrained with the precision achieved by

current SNIa and BAO surveys, while in the futuristic case ($N_{rm

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 $N_{rm lens}=20$. Both

approaches learn effectively from the features of the mock data points,

yielding $1sigma$ constraints that are in excellent agreement with the

parameterised results.

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