A thorough investigation of the prospects of eLISA in addressing the Hubble tension: Fisher Forecast, MCMC and Machine Learning

Abstract

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.

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

“…The MCMC constraints for each model corresponding to data Set-I have already been investigated partially by the present authors Shah et al (2023) and partially by others Di Valentino et al (2020). We simply quote the results here in Table 2.…”

“…In order to get rid of any potential bias from a particular mock catalogue, we generate 500 mock catalogues of observable bright siren events for each case of our study (see Table 1). We also make some modifications to the methodology outlined in Ferreira et al (2022) to make the catalogues more realistic as mentioned in Shah et al (2023). Here is a brief outline of our adopted methodology:…”

“…Constraints from nextgeneration GW mission data are expected to be much more precise due to significantly higher numbers of detectable events up to higher redshifts. However, most of the predicted results show dependence on the choice of cosmological parameters when real data is absent and forecasts are carried out using mission-specific mock standard siren catalogues (Shah et al 2023).…”

“…GP is also being extensively used in computational chemistry and material sciences (Deringer et al 2021;Sabin et al 2000), nonlinear dynamics (Wang et al 2005), condensed matter physics (Raimbault et al 2019;Rath & Booth 2022), and astrophysics (Bu et al 2020;Aigrain & Foreman-Mackey 2022). Over the last decade, GP has become particularly popular in cosmology for reconstructing dark energy (Holsclaw et al 2011;Seikel et al 2012;Zhang & Li 2018), in cosmographic studies (Shafieloo et al 2012;Mukherjee & Banerjee 2021a;Jesus et al 2022), for exploring the interaction between dark matter and dark energy (Yang et al 2015;Mukherjee & Banerjee 2021b;Cai et al 2017), for testing the standard concordance model and distance duality relation (Nair et al 2015;Rana et al 2017;Mukherjee & Mukherjee 2021;Mukherjee et al 2023), for constraining spatial curvature (Yang & Gong 2021;Dhawan et al 2021;Mukherjee & Banerjee 2022), and in regression problems in modified theories of gravity (Zhou et al 2019;Belgacem et al 2020;Yang 2021;Bernardo & Levi Said 2021). For a pedagogical introduction to GP, one can refer to the Gaussian process website 1 .…”

“…Latest constraints on the cosmological model parameters using combined CMB+Pantheon+BAO (CSB) observational data (constraints marked with † have been quoted fromShah et al (2023), and * from Di Valentino et al (2020)).…”