A self-consistent system of gravitational field with a binary mixture of perfect fluid and dark energy given by a cosmological constant has been considered in Bianchi Type-V universe. The perfect fluid is chosen to be obeying either the equation of state p=γρ with γ ε |0,1| or a van der Waals equation of state. The role of A-term in the evolution of the Bianchi Type-V universe has been studied.

We have shown that, within the context of scalar-tensor theories, the anisotropic Bianchi-type cosmological models evolve towards de Sitter Universe. A similar result holds in the case of cosmology in Lyra manifold. Thus the analogue of cosmic no-hair theorem of Wald [1] hold in both the cases. In fact, during inflation there is no difference between scalar-tensor theories, Lyra’s manifold and general relativity (GR).

The general class of Bianchi cosmological models with dark energy in the form of modified Chaplygin gas with variable $\Lambda$ and $G$ and bulk viscosity have been considered. We discuss three types of average scalefactor by using a special law for deceleration parameter which is linear in time with negative slope. The exact solutions to the corresponding field equations are obtained. We obtain the solution of bulk viscosity ($\xi$ ), cosmologicalconstant ($\Lambda$), gravitational parameter ($G$) and deceleration parameter ($q$) for different equations of state. The model describes an accelerating Universe for large value of time $t$ , wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.

The general class of anisotropic Bianchi cosmological models in $f(R, T)$ modified theories of gravity with $\Lambda (T)$ has been considered. This paper deals with $f(R, T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar $R$ and the trace of the stress-energy tensor $T$ has been investigated for a specific choice of $f (R,T )$ = $f_{1}(R) + f_{2}(T)$. The exact solutions to the corresponding field equations are obtained in quadrature form. We have discussed three types of solutions of the average scale factor for the general class of Bianchi cosmological models by using a special law for deceleration parameter which is linear in time with a negative slope. The solutions to the Einstein field equations are obtained for three differentphysical viable cosmologies. All physical parameters are calculated and discussed in each model.

In this paper, we have studied the locally rotationally symmetric (LRS) Bianchi type-I cosmological model filled with a bulk viscous cosmological fluid in $f(R)$ gravity in the presence of time-varying gravitational and cosmological constant. We have used the power-law and intermediate scenario for scale factor to obtain thesolution of the field equations. The evolution of temperature of a viscous Universe is also analysed.

In this paper, we deal with a Finsler–Randers (FR) cosmology in the framework of particle creation mechanism. The cosmological history of the model is studied by finding all the critical points and analysing their local stability.We study the behaviour of all critical points of the model when they are non-hyperbolic in nature using the centre manifold theory. The perseverance of the equilibrium points are illustrated by showing the vector field locally near the equilibrium point. The possible bifurcation scenarios are discussed in detail with the help of local bifurcation diagrams for each of the critical points. Concluding remarks and the cosmological upshot are also given.

In this paper, we deal with locally rotationally symmetric Bianchi type-$I$cosmological model with varying cosmological constant. Here, we have considered two models. In Model $I$, we have analysed total linear stability analysis for linear coupling between the dark sector of the Universe where as in Model $II$, the quadratic coupling between the dark sector of the Universe is considered. The cosmological history of the models is studied by finding all the critical points and analysing their local stability. We study the behaviour of all the critical points of the model when they are hyperbolic in nature using the linear Jacobi stability analysis and when they are non hyperbolic in nature using centre manifold theory. The perseverance of the equilibrium points is illustrated in phase portraits.