The cosmological jerk parameter j is reconstructed in a non-parametric way from observational data independent of a fiducial cosmological model. The Cosmic Chronometer data as well as the Supernovae data (the Pantheon compilation) are used for the purpose. The reconstructed values are found to be consistent with the standard $$\Lambda $$Λ CDM model within the $$2\sigma $$2 σ confidence level. The model dependent sets like Baryon Acoustic Oscillation and the CMB Shift data are also included thereafter, which does not significantly help in improving or de-proving the confidence level in favour of $$\Lambda $$Λ CDM. The deceleration parameter q is also reconstructed from the same data sets. This is used to find the effective equation of state parameter for the model independent datasets only. $$\Lambda $$Λ CDM model is excluded for some part of the evolution in $$1\sigma $$1 σ , but is definitely included in $$2\sigma $$2 σ in the domain ( $$0 \le z \le 2.36$$0 ≤ z ≤ 2.36 ) of all the reconstructions.

Two types of distance measurement are important in cosmological observations, the angular diameter distance d_A and the luminosity distance d_L. In this work, we carried out an assessment of the theoretical relation between these two distance measurements, namely the cosmic distance–duality relation, from type Ia supernova (SN-Ia) data, the cosmic chronometer (CC) Hubble parameter data, and baryon acoustic oscillation (BAO) data using Gaussian Process (GP). The luminosity distance curve and the angular diameter distance curve are extracted from the SN-Ia data and the combination of BAO and CC data, respectively, using the GP. The distance duality relation is checked by a non-parametric reconstruction using the reconstructed H, d_L, and the volume-averaged distance D_v. We compare the results obtained for different choices of the covariance function employed in the GP. It is observed that the theoretical distance duality relation is in well agreement with the present analysis in 2σ for the overlapping redshift domain 0 ≤ z ≤ 2 of the reconstruction.

The cosmic curvature density parameter has been constrained in the present work independent of any background cosmological model. The reconstruction is undertaken adopting the nonparametric Gaussian processes (GP). The constraints on ${\mathrm{\Omega }}_{k0}$ are obtained via a Markov Chain Monte Carlo (MCMC) analysis. Late-time cosmological probes viz., the supernova (SN) distance modulus data, the cosmic chronometer (CC) and the radial baryon acoustic oscillations ($r\mathrm{BAO}$) measurements of the Hubble data have been utilized for this purpose. The results are further combined with the data from redshift space distortions (RSD) which studies the growth of large scale structure in the universe. The only a priori assumption is that the universe is homogeneous and isotropic, described by the Friedmann-Lemaître-Robertson-Walker metric. Results indicate that a spatially flat universe is well consistent in $2\sigma$ within the domain of reconstruction $0<z<2$ for the background data. On combining the RSD data we find that the results obtained are consistent with spatial flatness mostly within $2\sigma$ and always within $3\sigma$ in the domain of reconstruction $0<z<2$.

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.