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 a primary focus on observations at intermediate redshifts (3 < z < 8). We consider six different parametrizations representing different classes of cosmological models, which we constrain using the latest datasets of cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and type Ia supernovae (SNIa) observations, in order to find out the up-to-date tensions with direct measurement data. Subsequently, these constraints are used as fiducials to construct mock catalogs for eLISA. We then employ Fisher analysis to forecast the future performance of each model in the context of eLISA. We further implement traditional Markov Chain Monte Carlo (MCMC) to estimate the parameters from the simulated catalogs. Finally, we utilize Gaussian Processes (GP), a machine learning algorithm, for reconstructing the Hubble parameter directly from simulated data. Based on our analysis, we present a thorough comparison of the three methods as forecasting tools. Our Fisher analysis confirms that eLISA would constrain the Hubble constant (H 0) at the sub-percent level. MCMC/GP results predict reduced tensions for models/fiducials which are currently harder to reconcile with direct measurements of H 0, whereas no significant change occurs for models/fiducials at lesser tensions with the latter. This feature warrants further investigation in this direction.

We examine the modulus stabilization mechanism of a warped geometry model with nested warping. Such a model with multiple moduli is known to offer a possible resolution of the fermion mass hierarchy problem in the standard model. A six dimensional doubly warped braneworld model under consideration admits two distinct moduli, with the associated warp factors dynamically generating different physical mass scales on four 3-branes. In order to address the hierarchy problem related to the Higgs mass, both moduli need to be stabilized around their desired values without any extreme fine tuning of parameters. We show that it is possible to stabilize them simultaneously due to the appearence of an effective 4D moduli potential, which is generated by a single bulk scalar field having non-zero VEVs frozen on the 3-branes. We also discuss how the entire mechanism can possibly be understood from a purely gravitational point of view, with higher curvature f (R) contributions in the bulk automatically providing a scalar degree of freedom that can serve as the stabilizing field in the Einstein frame.

We examine the modulus stabilization mechanism of a warped geometry model with nested warping. Such a model with multiple moduli is known to offer a possible resolution of the fermion mass hierarchy problem in the Standard Model. A six dimensional doubly warped braneworld model under consideration admits two distinct moduli, with the associated warp factors dynamically generating different physical mass scales on four 3-branes. In order to address the hierarchy problem related to the Higgs mass, both moduli need to be stabilized around their desired values without any extreme fine tuning of parameters. We show that it is possible to stabilize them simultaneously due to the appearence of an effective 4D moduli potential, which is generated by a single massive bulk scalar field having non-zero VEVs frozen on the 3-branes. This gives rise to two scalar radions, one of which has mass slightly below $${\mathcal {O}}$$ O (TeV) and couplings to SM fields proportional to the inverse of its $${\mathcal {O}}$$ O (TeV) VEV, and the other has nearly $${\mathcal {O}}(M_{Pl})$$ O ( M Pl ) mass and interactions with SM fields suppressed by the Planck scale. We also discuss how the entire mechanism can possibly be understood from a purely gravitational point of view, with higher curvature f(R) contributions in the bulk automatically providing a scalar degree of freedom that can serve as the stabilizing field in the Einstein frame.