Cylindrically Symmetric Inhomogeneous Universes with a Cloud of Strings

Cylindrically symmetric inhomogeneous string cosmological models are investigated in presence of string fluid as a source of matter. To get the three types of exact solutions of Einstein's field equations we assume $A = f(x)k(t)$, $B = g(x)\ell(t)$ and $C = h(x)\ell(t)$. Some physical and geometric aspects of the models are discussed.Comment: 9 page

String cosmological model in the presence of a magnetic flux

A Bianchi type I string cosmological model in the presence of a magnetic flux is investigated. A few plausible assumptions regarding the parametrization of the cosmic string and magneto-fluid are introduced and some exact analytical solutions are presented.Comment: 9 pages, 4 Figure

A New Class of Inhomogeneous String Cosmological Models in General Relativity

A new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source. To get the deterministic solution, it has been assumed that the expansion ($\theta$) in the model is proportional to the eigen value $\sigma^{1}_{1}$ of the shear tensor $\sigma^{i}_{j}$. Certain physical and geometric properties of the models are also discussed.Comment: 12 pages, no figure. Submitted to Astrophys. Space Sci. arXiv admin note: substantial text overlap with arXiv:0705.090

Lyra's Cosmology of Massive String in Anisotropic Bianchi-II Space-time

The paper deals with a spatially homogeneous and totally anisotropic Bianchi II cosmological models representing massive strings in normal gauge for Lyra's manifold. The modified Einstein's field equations have been solved by applying variation law for Hubble's parameter. This law generates two type of solutions for average scale factor, one is of power law type and other is of exponential law type. The power law describes the dynamics of Universe from big bang to present epoch while exponential law seems reasonable to project dynamics of future Universe. It has been found that the displacement actor $(\beta)$ is a decreasing function of time and it approaches to small positive value at late time, which is collaborated with Halford (1970) as well as recent observations of SN Ia. The study reveals that massive strings dominate in early Universe and eventually disappear from Universe for sufficiently large time, which is in agreement with the current astronomical observations.Comment: 12 pages, 5 figure

Bulk Viscous LRS Biachi-I Universe with variable GG and decaying Λ\Lambda

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.Comment: 11 pages, 4 figures and 1 table, Accepted for publication in Astrophysics and Space Scienc

Some Bianchi Type III String Cosmological Models with Bulk Viscosity

We investigate the integrability of cosmic strings in Bianchi III space-time in presence of a bulk viscous fluid by applying a new technique. The behaviour of the model is reduced to the solution of a single second order nonlinear differential equation. We show that this equation admits an infinite family of solutions. Some physical consequences from these results are also discussed.Comment: 12 pages, no figure. To appear in Int. J. Theor. Phy

Bianchi Type-I Cosmological Models with Variable G and 4\Lambda$-Terms in General Relativity

Einstein's field equations with variable gravitational and cosmological ``constant'' are considered in presence of perfect fluid for Bianchi type-I spacetime. Consequences of the four cases of the phenomenological decay of $\Lambda$ have been discussed which are consistent with observations. The physical significance of the cosmological models have also been discussed.Comment: 12 pages, no figur

Bianchi type-I model with cosmic string in the presence of a magnetic field: spinor description

A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmic string is investigated. A nonlinear spinor field is used to simulate the cosmological cloud of strings. It is shown that the spinor field simulation offer the possibility to solve the system of Einstein's equation without any additional assumptions. It is shown that the present model is nonsingular at the end of the evolution and does not allow the anisotropic Universe to turn into an isotropic one.Comment: 14 pages, 4 figures, new figus are added, singularity and isotropization process are discussed in detai

Bianchi type-I string cosmological model in the presence of a magnetic field: classical versus loop quantum cosmology approaches

A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmological string is considered. The first objective of this study is to investigate Einstein equations using a tractable assumption usually accepted in the literature. Quantum effects of the present cosmological model are examined in the framework of loop quantum cosmology. Finally we draw a parallel between the classical and quantum approaches.Comment: 14 pages, 8 figure

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics