We consider a scenario of modified gravity, which is generic to late-time acceleration, namely, acceleration in the Jordan frame and no acceleration in the Einstein frame. The possibility is realized by assuming an interaction between dark matter and the baryonic component in the Einstein frame which is removed by going to the Jordan frame using a disformal transformation giving rise to an exotic effective fluid responsible for causing phantom crossing at late times. In this scenario, past evolution is not distinguished from $\mathrm{\Lambda }\mathrm{CDM}$ but late time dynamics is generically different due to the presence of phantom crossing that causes a monotonous increase in the expansion rate giving rise to distinctive late-time cosmic feature. The latter can play a crucial role in addressing the tension between the observed value of Hubble parameter by CMB (cosmic microwave background) measurements and the local observations. We demonstrate that the Hubble tension significantly reduces in the scenario under consideration for the chosen scale factor parametrizations. The estimated age of the universe in the model is well within the observational bounds in the low and high redshift regimes.

We study the late-time cosmological tensions using the low-redshift background and redshift-space distortion data by employing a machine learning (ML) technique. By comparing the generated observables with the standard cosmological scenario, our findings indicate support for the phantom nature of dark energy, which ultimately leads to a reduction in the existing tensions. The model-independent approach also enables us to examine the combined background and perturbative history, where tensions are reduced. Moreover, from a statistical perspective, we have shown that our results exhibit a better fit to the data when compared to the $\mathrm{\Lambda }\mathrm{CDM}$ model.

We consider the framework of quintessential inflation in the warm background which is caused by the dissipation of the scalar field energy density into relativistic degrees of freedom. The dissipation process has important consequences for the evolution both at the levels of background as well as perturbation and allows us to easily satisfy the observational constraints. Our numerical analysis confirms that the model conforms to observational constraints even if the field-radiation coupling strength is weak. In the warm background, we investigate the postinflationary evolution of relic gravity waves produced during inflation whose amplitude is constrained by the big bang nucleosynthesis constraint. Further, we investigate the effect of coupling on the amplitude of gravity waves and obtain the allowed phase space between the model parameters. The mechanism of quintessential inflation gives rise to blue spectrum of gravitational wave background at high frequencies. We discuss the perspectives of detection of the signal of relic gravity waves by future proposed missions. Improvements of their sensitivities in the high frequency regime, in future, might allow us to probe the blue tilt of the spectrum caused by the presence of kinetic regime in the underlying framework of inflation.

We study the growth of linear matter density perturbations in a modified gravity approach of scalar field couplings with metric and torsion. In the equivalent scalar-tensor formulation, the matter fields in the Einstein frame interact as usual with an effective dark energy component, whose dynamics are presumably governed by a scalar field that sources a torsion mode. As a consequence, the matter density ceases to be self-conserved, thereby making an impact not only on the background cosmological evolution but also on the perturbative spectrum of the local inhomogeneities. In order to estimate the effect on the growth of the linear matter perturbations, with the least possible alteration of the standard parametric form of the growth factor, we resort to a suitable Taylor expansion of the corresponding exponent, known as the growth index, about the value of the cosmic scale factor at the present epoch. In particular, we obtain an appropriate fitting formula for the growth index in terms of the coupling function and the matter density parameter. While the overall parametric formulation of the growth factor is found to fit well with the latest redshift-space-distortion (RSD) and the observational Hubble (OH) data at low redshifts, the fitting formula enables us to constrain the growth index to well within the concordant cosmological limits, thus ensuring the viability of the formalism.

We study the possibility of accommodating both early and late-time tensions using a novel reinforcement learning technique. By applying this technique, we aim to optimize the evolution of the Hubble parameter from recombination to the present epoch, addressing both tensions simultaneously. To maximize the goodness of fit, our learning technique achieves a fit that surpasses even the ΛCDM model. Our results demonstrate a tendency to weaken both early and late time tensions in a completely model-independent manner.