We have considered the FRW universe in loop quantum cosmology (LQC) model filled with the dark matter (perfect fluid with negligible pressure) and the modified Chaplygin we concluded that our model is in agreement with the union2 sample data.

In this work, we have calculated the deceleration parameter, statefinder parameters and EoS parameters for different dark energy models with variable G correction in homogeneous, isotropic and non-flat universe for Kaluza-Klein Cosmology. The statefinder parameters have been obtained in terms of some observable parameters like dimensionless density parameter, EoS parameter and Hubble parameter for holographic dark energy, new agegraphic dark energy and generalized Chaplygin gas models. Contents

We have considered N -dimensional Einstein field equations in which fourdimensional space-time is described by a FRW metric and that of extra dimensions by an Euclidean metric. We have supposed that the higher dimensional anisotropic universe is filled with only normal scalar field or tachyonic field. Here we have found the nature of potential of normal scalar field or tachyonic field. From graphical representations, we have seen that the potential is always decreases with field φ increases.Keywords Higher dimensions · Acceleration · Scalar field · Tachyonic fieldRecently the most interesting problems of particle physics cosmology is the origin of accelerated expansion of the present universe. From astronomical observations it is evident that the present day universe has the critical energy density containing about 70% dark energy and 30% dark matter, responsible for cosmic acceleration [1]. From string/M-theory or braneworld model recently many cosmological models have been constructed by introducing quintessence, dilaton or antisymmetric tensor field. On the other hand dark energy models are basically based on holographic principle developed by AdS/CFT.To understand the current quintessential behavior the existence of extra dimensions is very much necessary like dark energy and dark matter. Model of higher dimension was proposed by Kaluza and Klein [2, 3] who tried to unify gravity with electromagnetic interaction by introducing an extra dimension which is basically an extension of Einstein general

In this work, we have considered that the anisotropic universe is filled with normal matter and phantom field (or tachyonic field). We have chosen the exponential forms of scale factors a and b in such a way that there is no singularity for evolution of the anisotropic universe. Here we have shown that the emergent scenario is possible for open, closed or flat universe if the universe contains phantom field or tachyonic field or phantom tachyonic field. From recently developed statefinder parameters, the behaviour of different stages of the evolution of the emergent universe have been generated.Keywords Emergent scenario · Anisotropic universe · Tachyonic field One of the fundamental questions of modern cosmology is whether the universe had a definite origin or whether it is past eternal. Recently, Ellis and Maartens [1] have considered a cosmological model where inflationary cosmologies exist in which the horizon problem is solved before inflation begins, no big-bang singularity exist, no exotic physics is involved and quantum gravity regime can even be avoided. The emergent universe scenario occurs when the inflationary universe emerges from a small static state that has within it the seeds for the development of the microscopic universe. An emergent universe model if developed in a consistent way is capable of solving the conceptual problems of the big-bang model. Actually the universe starts out in the infinite past as an almost static universe and expands slowly, eventually evolving into a hot big-bang era. In [2] we have seen an interesting example of this scenario for a closed universe model with a minimally coupled scalar field φ

In this work, we have consider Kaluza-Klein Cosmology for anisotropic universe where the universe is filled with variable modified chaplygin gas (VMCG). Here we find normal scalar field φ and the self interacting potential V (φ) to describe the VMCG Cosmology. Also we graphically analyzed the geometrical parameters named statefinder parameters in anisotropic Kaluza-Klein model. Next, we consider a Kaluza-Klein model of interacting VMCG with dark matter in the Einstein gravity framework. Here we construct the three dimensional autonomous dynamical system of equations for this interacting model with the assumption that the dark energy and the dark matter are interact between them and for that we also choose the interaction term. We convert that interaction terms to its dimensionless form and perform stability analysis and solve them numerically. We obtain a stable scaling solution of the equations in Kaluza-Klein model and graphically represent solutions.