Reconstructing the Hubble parameter with future Gravitational Wave missions using Machine Learning

We study the prospects of Machine Learning algorithms like Gaussian processes (GP) as a tool to reconstruct the Hubble parameter $H(z)$ with two upcoming gravitational wave missions, namely the evolved Laser Interferometer Space Antenna (eLISA) and the Einstein Telescope (ET). We perform non-parametric reconstructions of $H(z)$ with GP using realistically generated catalogues, assuming various background cosmological models, for each mission. We also take into account the effect of early-time and late-time priors separately on the reconstruction, and hence on the Hubble constant ($H_0$). Our analysis reveals that GPs are quite robust in reconstructing the expansion history of the Universe within the observational window of the specific mission under study. We further confirm that both eLISA and ET would be able to constrain $H(z)$ and $H_0$ to a much higher precision than possible today, and also find out their possible role in addressing the Hubble tension for each model, on a case-by-case basis.