We carry out an in-depth analysis of the capability of the upcoming space-based gravitational wave mission eLISA in addressing the Hubble tension, with primary focus on observations at intermediate redshifts (3 < z < 8). We consider six different parametrisations representing different classes of cosmological models, which we constrain using the latest datasets of CMB + BAO + SNIa, to find out the up-to-date tensions with direct measurement data. Subsequently, these constraints are used to construct mock catalogues for eLISA. We then employ a three-pronged approach involving Fisher analysis, Markov Chain Monte Carlo, and Machine Learning using Gaussian Processes on the simulated catalogues to forecast on the future performance of each model. Based on our analysis, we present a thorough comparison among the three methods as forecasting tools, as well as among the different models predicted by each method. Our analysis confirms that eLISA would constrain H 0 at the sub-percent level. MCMC and GP results predict reduced tensions for models which are currently harder to reconcile with direct measurements of H 0 , whereas no significant change occurs for models at lesser tensions with the latter. This feature warrants further investigation in this direction.

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.