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 (H0β). 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
H0β 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.Comment: 9 pages, 5 sets of figure