We have studied Locally Rotationally Symmetric (LRS) Bianchi type-I
cosmological model filled with anisotropic fluid in general theory of
relativity. The solutions of the field equations are obtained by using special
form of deceleration parameter which gives early deceleration and late time
accelerating cosmological model. The geometrical and physical aspect of the
model is also studied.

Abstract:
In this paper we have investigated an LRS Bianchi I anisotropic cosmological model of the universe by taking time varying $G$ and $\Lambda$ in the presence of bulk viscous fluid source described by full causal non-equilibrium thermodynamics. We obtain a cosmological constant as a decreasing function of time and for $m, n > 0$, the value of cosmological ``constant'' for this model is found to be small and positive which is supported by the results from recent supernovae observations.

Abstract:
Locally rotationally symmetric (LRS) Bianchi Type I cosmological models are examined in the presence of dynamically anisotropic dark energy and perfect fluid. We assume that the dark energy (DE) is minimally interacting, has dynamical energy density, anisotropic equation of state parameter (EoS). The conservation of the energy-momentum tensor of the DE is assumed to consist of two separately additive conserved parts. A special law is assumed for the deviation from isotropic EoS, which is consistent with the assumption on the conservation of the energy-momentum tensor of the DE. Exact solutions of Einstein's field equations are obtained by assuming a special law of variation for the mean Hubble parameter, which yields a constant value of the deceleration parameter. Geometrical and kinematic properties of the models and the behaviour of the anisotropy of the dark energy has been carried out. The models give dynamically anisotropic expansion history for the universe that allows to fine tune the isotropization of the Bianchi metric, hence the CMB anisotropy.

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:
We investigate locally rotational symmetric (LRS) Bianchi type I space time coupled with scalar field. String cosmological models generated by a cloud of strings with particles attached to them are studied in the Brans-Dicke theory. We assume that the expansion scalar is proportional to the shear scalar and also power law ansatz for scalar field. The physical behavior of the resulting model is discussed through different parameters. 1. Introduction It is believed that the early universe evolved through some phase transitions, thereby yielding a vacuum energy density which at present is at least 118 orders of magnitudes smaller than in the Planck time [1]. Such a discrepancy between theoretical expectations and empirical observations constitutes a fundamental problem in the interface uniting astrophysics, particle physics, and cosmology. The recent observational evidence for an accelerated state of the present universe, obtained from distant SNe Ia (Perlmutter et al. [2]; Riess et al. [3]), gave strong support to search for alternative cosmologies. Thus, the state of affairs has stimulated the interest in more general models containing an extra component describing dark energy and simultaneously accounting for the present accelerated stage of the universe. The isotropic models are considered to be the most suitable to study large scale structure of the universe. However, it is believed that the early universe may not have been exactly uniform. This prediction motivates us to describe the early stages of the universe with the models having anisotropic background. Thus, it would be worthwhile to explore anisotropic models in the context of modified theories of gravity. Among the various modifications of general relativity (GR), the Brans-Dicke (BD) theory of gravity [4] is a well-known example of a scalar tensor theory in which the gravitational interaction involves a scalar field and the metric tensor. One extra parameter is used in this theory which satisfies the equation given by where is known as BD scalar field while is the trace of the matter energy-momentum tensor. It is mentioned here that the general relativity is recovered in the limiting case . Thus we can compare our results with experimental tests for significantly large value of . The majority of popular cosmological models, including all the ones referred to above, use the cosmological principle; that is, they assume that the universe is homogeneous and isotropic. On the other hand, there are hints in the CMB temperature anisotropy studies that suggest that the assumption of statistical

Abstract:
An LRS Bianchi type-V cosmological models representing a viscous fluid distribution with a time dependent cosmological term $\Lambda$ is investigated. To get a determinate solution, the viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. It turns out that the cosmological term $\Lambda(t)$ is a decreasing function of time, which is consistent with recent observations of type Ia supernovae. Various physical and kinematic features of these models have also been explored.

Abstract:
The present study deals with LRS Bianchi type I cosmological model representing massive string. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the shear scalar ($\sigma$) is proportional to the expansion scalar ($\theta$). The study reveals that massive strings dominate the early Universe. The strings eventually disappear from the Universe for sufficiently large time, which is in agreement with the current astronomical observations. Some physical and geometrical behaviour of models are also discussed.

Abstract:
LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra's geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter models of the universe. We have compared our models with those of Einstein's field theory with the cosmological term $\Lambda$. Our frame of reference is restricted to the recent Ia observations of supernovae. Some physical behaviour of the models is also examined in the presence of perfect fluids.

Abstract:
The present study deals with locally rotationally symmetric (LRS) Bianchi type II cosmological models representing massive string. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the expansion ($\theta$) in the models is proportional to the shear ($\sigma$). This condition leads to $A = B^{m}$, where A and B are the metric coefficients and m is constant. We have derived two types of models depending on different values of m i.e. for $m\neq \sqrt{2}$ and $m = \sqrt{2}$ respectively. For suitable choice of constant m (i.e. for $m = 1/2$), it is observed that in early stage of the evolution of the universe, the universe is dominated by strings in both cases. Our models are in accelerating phase which is consistent to the recent observations of type Is supernovae. Some physical and geometric behaviour of the models are also discussed.