Abstract:
in this paper we present a spatially homogeneous locally rotationally symmetric (lrs) bianchi type -v perfect fluid model with heat conduction in scalar tensor theory proposed by saez and ballester. the field equations are solved with and without heat conduction by using a law of variation for the mean hubble parameter, which is related to the average scale factor of metric and yields a constant value for the deceleration parameter. the law of variation for the mean hubble parameter generates two types of cosmologies one is of power -law form and second the exponential form. using these two forms singular and non -singular solutions are obtained with and without heat conduction. we observe that a constant value of the deceleration parameter is reasonable a description of the different phases of the universe. we arrive to the conclusion that the universe decelerates for positive value of deceleration parameter where as it accelerates for negative one. the physical constraints on the solutions of the field equations, and, in particular, the thermodynamical laws and energy conditions that govern such solutions are discussed in some detail.the behavior of the observationally important parameters like expansion scalar, anisotropy parameter and shear scalar is considered in detail.

Abstract:
A new class of LRS Bianchi type ${\rm VI}_{0}$ cosmological models with free gravitational fields and a variable cosmological term is investigated in presence of perfect fluid as well as bulk viscous fluid. To get the deterministic solution we have imposed the two different conditions over the free gravitational fields. In first case we consider the free gravitational field as magnetic type whereas in second case `gravitational wrench' of unit `pitch" is supposed to be present in free gravitational field. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. The cosmological constant $\Lambda$ is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. The physical and geometric aspects of the models are discussed.

Abstract:
It is investigated the behaviour of the ``constants'' $G,$ $c$ and $\Lambda $ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a $c-$variable into the curvature tensor. Two exact cosmological solutions are investigated, arriving to the conclusion that if $q<0$ (deceleration parameter) then $G,$ $c$ are growing functions on time $t$ while $\Lambda $ is a negative decreasing function on time.

Abstract:
In this paper we study the evolution of a LRS Bianchi I Universe, filled with a bulk viscous cosmological fluid in the presence of time varying constants "but" taking into account the effects of a c-variable into the curvature tensor. We find that the only physical models are those which ``constants'' $G$ and $c$ are growing functions on time $t$, while the cosmological constant $\Lambda$ is a negative decreasing function. In such solutions the energy density obeys the ultrastiff matter equation of state i.e. $\omega=1$.

Abstract:
The present study deals with spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dominance of dark energy. To get the deterministic model of Universe, we assume that the shear scalar $(\sigma)$ in the model is proportional to expansion scalar $(\theta)$. This condition leads to $A=B^{n}$, where $A$,\;$B$ are metric potential and $n$ is positive constant. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of Universe. The physical behavior of the Universe has been discussed in detail.

Abstract:
Locally rotationally symmetric (LRS) Bianchi type-I dark energy cosmological model with variable equation of state (EoS) parameter in (Nordtvedt 1970) general scalar tensor theory of gravitation with the help of a special case proposed by (Schwinger 1970) is obtained. It is observed that these anisotropic and isotropic dark energy cosmological models always represent an accelerated universe and are consistent with the recent observations of type-Ia supernovae. Some important features of the models, thus obtained, have been discussed. 1. Introduction Nordtvedt [1] proposed a general class of scalar tensor gravitational theories in which the parameter of the Brans-Dicke (BD) theory is allowed to be an arbitrary (positive definite) function of the scalar field ( ). Considering the static spherically symmetric solution for a point mass source, Nordtvedt [1] found a variety of experimental consequences of , including a contribution to the rate of precession of Mercury’s perihelion. Several investigations have been made in higher dimensional cosmology in the framework of different scalar tensor theories of gravitation. Barker [2], Ruban and Finkelstein [3], Banerjee and Santos [4, 5], and Shanti and Rao [6, 7] are some of the authors who have investigated several aspects of the Nordtvedt general scalar tensor theory in four dimensions. Rao and Sreedevi Kumari [8] have discussed a cosmological model with negative constant deceleration parameter in a general scalar tensor theory of gravitation. Rao et al. [9] have obtained the Kaluza-Klein radiating model in a general scalar tensor theory of gravitation. Rao et al. [10] have discussed LRS Bianchi type-I dark energy cosmological model in the Brans-Dicke theory of gravitation. Rao et al. [11] have discussed Bianchi type-II, -VIII, and -IX dark energy cosmological models in the Saez-Ballester theory of gravitation. Recently, Rao et al. [12] have obtained perfect fluid dark energy cosmological models in the Saez-Ballester and general theory of gravitation. Recently, there has been considerable interest in cosmological models with dark energy in general relativity because of the fact that our universe is currently undergoing an accelerated expansion which has been confirmed by a host of observations, such as type Ia supernovae (Reiss et al. [13]; Perlmutter et al. [14]; and Tegmark et al. [15]). Based on these observations, cosmologists have accepted the idea of dark energy, which is a fluid with negative presence making up around 70% of the present universe energy content to be responsible for this acceleration due

Abstract:
In this paper we report on results in the study of spatially homogeneous cosmological models with elastic matter. We show that the behavior of elastic solutions is fundamentally different from that of perfect fluid solutions already in the case of locally rotationally symmetric (LRS) Bianchi type I models; this is true even when the elastic material resembles a perfect fluid very closely. In particular, the approach to the initial singularity is characterized by an intricate oscillatory behavior of the scale factors, while the future asymptotic behavior is described by isotropization rates that differ significantly from those of perfect fluids.

Abstract:
The present study deals with spatially homogeneous and totally anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with variable $G$ and $\Lambda$ in presence of imperfect fluid. To get the deterministic model of Universe, we assume that the expansion $(\theta)$ in the model is proportional to shear $(\sigma)$. This condition leads to $A=\ell B^{n}$, where $A$,\;$B$ are metric potential. The cosmological constant $\Lambda$ is found to be decreasing function of time and it approaches a small positive value at late time which is supported by recent Supernovae Ia (SN Ia) observations. Also it is evident that the distance modulus curve of derived model matches with observations perfectly.

Abstract:
At the present paper, Locally Rotationally Symmetric (LRS) Bianchi type-II cosmological model with interacting dark matter (DM) and holographic dark energy (DE) have been discussed. In order to obtain solutions of the field equations, it is assume that the shear scalar (σ) is proportional to expansion scalar (θ). To have a general description of holographic dark energy and dark matter, a phenomenological parameterization of dark energy in terms of its equation of state (EoS) has been taken. Statefinder diagnostic pair i.e.｛r, s｝is adopted to separate other existing dark energy models from this model. Here we discuss two models: when n=1/2, we obtain acyclic universe and the model converges into phantom region whereas when n=3/2, we get a expanding universe and the model converges into quintessence region. Some important geometrical and physical features regarding to this model have also been studied.

Abstract:
The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential volumetric expansion within the frame work of Lyra manifold for uniform and time varying displacement field. The isotropy of the fluid and space is examined.