Possible interaction between dark energy and dark matter has previously shown promise in alleviating the clustering tension, without exacerbating the Hubble tension, when Baryon Acoustic Oscillations (BAO) data from the Sloan Digital Sky Survey (SDSS) DR16 is combined with Cosmic Microwave Background (CMB) and Type-Ia Supernovae (SNIa) data sets. With the recent Dark Energy Spectroscopic Instrument (DESI) BAO DR2, there is now a compelling need to re-evaluate this scenario. We combine DESI DR2 with Planck 2018 and Pantheon + SNIa data sets to constrain interacting dark matter dark energy models, accounting for interaction effects in both the background and perturbation sectors. Our results exhibit similar trends to those observed with SDSS, albeit with improved precision, reinforcing the consistency between the two BAO data sets. In addition to offering a resolution to the $S_8$ tension, in the phantom-limit, the dark energy equation of state exhibits an early-phantom behaviour, aligning with DESI DR2 findings, before transitioning to $w\sim -1$ at lower redshifts, regardless of the DE parametrization. However, the statistical significance of excluding $w=-1$ is reduced compared to their non-interacting counterparts.

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 do a careful investigation of the prospects of dark energy (DE) interacting with cold dark matter in alleviating the $S_8$ clustering tension. To this end, we consider various well-known parametrizations of the DE equation of state (EoS) and consider perturbations in both the dark sectors, along with an interaction term. Moreover, we perform a separate study for the phantom and non-phantom regimes. Using cosmic microwave background (CMB), baryon acoustic oscillations, and Type Ia supernovae data sets, constraints on the model parameters for each case have been obtained and a generic reduction in the $H_0 \!\!-\!\! \sigma _{8,0}$ correlation has been observed, both for constant and dynamical DE EoS. This reduction, coupled with a significant negative correlation between the interaction term and $\sigma _{8,0}$, contributes to easing the clustering tension by lowering $\sigma _{8,0}$ to somewhere in between the early CMB and late-time clustering measurements for the phantom regime, for almost all the models under consideration. Additionally, this is achieved without exacerbating the Hubble tension. In this regard, the interacting Chevallier–Polarski–Linder and Jassal–Bagla–Padmanabhan models perform the best in relaxing the $S_8$ tension to $<\!\! 1\sigma$. However, for the non-phantom regime the $\sigma _{8,0}$ tension tends to have worsened, which reassures the merits of phantom DE from latest data. We further investigate the role of redshift space distortion data sets and find an overall reduction in tension, with a $\sigma _{8,0}$ value relatively closer to the CMB value. We finally check whether further extensions of this scenario, such as the inclusion of the sound speed of DE and warm dark matter interacting with DE, can have some effects.

We investigate the prospect of reconstructing the “cosmic distance ladder” of the Universe using a novel deep learning framework called LADDER—Learning Algorithm for Deep Distance Estimation and Reconstruction. LADDER is trained on the apparent magnitude data from the Pantheon Type Ia supernova compilation, incorporating the full covariance information among data points, to produce predictions along with corresponding errors. After employing several validation tests with a number of deep learning models, we pick LADDER as the best-performing one. We then demonstrate applications of our method in the cosmological context, including serving as a model-independent tool for consistency checks for other data sets like baryon acoustic oscillations, calibration of high-redshift data sets such as gamma-ray bursts, and use as a model-independent mock-catalog generator for future probes. Our analysis advocates for careful consideration of machine learning techniques applied to cosmological contexts.

We study the prospects of Gaussian processes (GPs), a machine-learning (ML) algorithm, as a tool to reconstruct the Hubble parameter H(z) with two upcoming gravitational-wave (GW) missions, namely, the evolved Laser Interferometer Space Antenna (eLISA) and the Einstein Telescope (ET). Assuming various background cosmological models, the Hubble parameter has been reconstructed in a nonparametric manner with the help of a GP using realistically generated catalogs for each mission. The effects of early-time and late-time priors on the reconstruction of H(z), and hence on the Hubble constant (H ₀), have also been focused on separately. Our analysis reveals that a GP is quite robust in reconstructing the expansion history of the Universe within the observational window of the specific missions under consideration. We further confirm that both eLISA and ET would be able to provide constraints on H(z) and H ₀, which would be competitive to those inferred from current data sets. In particular, we observe that an eLISA run of a ∼10 yr duration with ∼80 detected bright siren events would be able to constrain H ₀ as precisely as a ∼3 yr ET run assuming ∼1000 bright siren event detections. Further improvement in precision is expected for longer eLISA mission durations such as a ∼15 yr time frame having ∼120 events. Lastly, we discuss the possible role of these future GW missions in addressing the Hubble tension, for each model, on a case-by-case basis.