Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late-time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. The equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering Barrow HDE as a specific case of Nojiri–Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to −1 for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study. Finally, it has been observed that the model under consideration is very close to ΛCDM and cannot go beyond it.

Motivated by the work of Nojiri et al. [1], the present study reports a model of inflation under the consideration that the inflationary regime is originated by a type of holographic energy density. The infrared cutoff has been selected based on the modified holographic model that is a particular case of Nojiri-Odintsov holographic dark energy [13] that unifies phantom inflation with the acceleration of the universe on late-time. On getting an analytical solution for Hubble parameter we considered the presence of bulk viscosity and the effective equation of state parameter appeared to be consistent with inflationary scenario with some constraints. It has also being observed that in the inflationary scenario the contribution of bulk viscosity is not of much significance and its influence is increasing with the evolution of the universe. Inflationary observables have been computed for the model and the slow-roll parameters have been computed. Finally, it has been observed that the trajectories in n s − r are compatible with the observational bound found by Planck. It has been concluded that the tensor to scalar ratio for this model can explain the primordial fluctuation in the early universe as well.

The present study reports a reconstruction scheme for f (T) gravity under the assumption that the density due to the torsion T evolves like the variable-generalized Chaplygin gas (VGCG), a phenomenological candidate of dark energy. This reconstruction has been demonstrated in viscous as well as non-viscous cases. The state-finder trajectory {r − s} has been found to attain the ΛCDM fixed point under this reconstruction scenario. The reconstructed equation of state parameter (EoS) has been studied for their phantom/quintom behavior. The effect of bulk viscous pressure has been found to become prominent in the late stage. The generalized second law (GSL) of thermodynamics has been studied for Bekeinstein-Hawking entropy area relation in both non-viscous and viscous cases. The GSL is found to be valid in both cases.

The present study reports a reconstruction scheme of a Dark Energy (DE) model with higher order derivative of Hubble parameter, which is a particular case of Nojiri-Odintsov holographic DE [50] that unifies phantom inflation with the acceleration of te universe on late-time. The reconstruction has been carried out in presence of bulk-viscosity, where the bulk-viscous pressure has been taken as a function of Hubble parameter. Ranges of cosmic time t have been derived for quintessence, cosmological constant and phantom behaviour of the equation of state (EoS) parameter. In the viscous scenario, the reconstruction has been carried out in an interacting and non-interacting situations and in both the cases stability against small perturbations has been observed. Finally, the slow roll parameters have been studied and a scope of exit from inflation has been observed. Also, availability of quasi exponential expansion has been demonstrated for interacting viscous scenario and a study through tensor to scalar ratio has ensured consistency of the model with the observational bound by Planck. Alongwith primordial fluctuations the interacting scenario has been found to generate strong dissipative regime.

The work presented in this paper aims to study the inflationary cosmology of [Formula: see text] gravity where [Formula: see text] by two models of Dark Energy (DE), namely Variable Generalized Chaplygin Gas (VGCG) and the Nojiri–Odintsov Holographic Dark Energy. The reconstruction has been carried out in the absence as well as presence of viscosity. The viscous pressure is considered to be [Formula: see text], where [Formula: see text] and [Formula: see text] is the Hubble parameter. In viscous and nonviscous scenarios, the reconstruction has been carried out for power law scale factor and bounce scale factor. For the specific range of cosmic time [Formula: see text], the quintessence and quintom behavior are observed for the equation of state parameters. The slow roll parameters have been studied for both the cases in nonviscous scenario and for the case, namely bounce scale factor for VGCG of nonviscous scenario, we have found that there is a scope of exit from inflation. Furthermore, constraints have been deduced to study the presence of singularity. Finally, the [Formula: see text] gravity is reconstructed as a function of cosmic time [Formula: see text] and is found to stay at positive level for a range of cosmic time [Formula: see text].