Abstract:
We can solve the Wheeler-DeWitt equation of the enlarged Bianchi I as inhomogeneous type universe with static restriction which had been derived by previous paper. We consider the commutation relation between the static restriction and the Hamiltonian constraint. And we can simplify the usual 3+1 Hamiltonian constraint of the enlarged Biancki I type universe, and we finally show the state's form is the exponential. And we find that the states of the quantum gravity are entangled. Our paper based on the previous work of ours that we call up-to-down method which was aimed to simplify the Wheeler-DeWitt equation.

Abstract:
We present a cosmological landscape where the classical closed string tachyon field plays an important role in the framework of a critical bosonic compactification. Our cosmological solutions for a universe with constant curvature describes an finite inflationary stage which expands till a maximum value before undergoes a big crunch as the tachyon reaches the minimum of its potential.

Abstract:
We present a conformal field theory -- obtained from a gauged WZW model -- that describes a closed, inhomogeneous expanding and recollapsing universe in $3+1$ dimensions. A possible violation of cosmic censorship is avoided because the universe recollapses just when a naked singularity was about to form. The model has been chosen to have $c=4$ (or $\widehat c=4$ in the supersymmetric case), just like four dimensional Minkowski space.

Abstract:
We calculate the energy distribution of an anisotropic model of universe, based on the Bianchi type I metric, in the Tolman's prescription. The energy due to the matter plus gravitational field is equal to zero. This result agrees with the results of Banerjee and Sen and Xulu. Also, our result supports the viewpoint of Tryon and Rosen.

Abstract:
Extended Einstein-Maxwell model and its application to the problem of evolution of magnetized Bianchi-I Universe are considered. The evolution of medium magnetization is governed by a relaxation type extended constitutive equation. The series of exact solutions to the extended master equations is obtained and discussed. The anisotropic expansion of the Bianchi-I Universe is shown to become non-monotonic (accelerated/decelerated) in both principal directions (along the magnetic field and orthogonal to it). A specific type of expansion, the so-called evolution with hidden magnetic field, is shown to appear when the magnetization effectively screens the magnetic field and the latter disappears from the equations for gravitational field.

Abstract:
We examine the dynamical consequences of homogeneous cosmological magnetic fields in the framework of loop quantum cosmology. We show that a big-bounce occurs in a collapsing magnetized Bianchi I universe, thus extending the known cases of singularity-avoidance. Previous work has shown that perfect fluid Bianchi I universes in loop quantum cosmology avoid the singularity via a bounce. The fluid has zero anisotropic stress, and the shear anisotropy in this case is conserved through the bounce. By contrast, the magnetic field has nonzero anisotropic stress, and shear anisotropy is not conserved through the bounce. After the bounce, the universe enters a classical phase. The addition of a dust fluid does not change these results qualitatively.

Abstract:
Considering Bianchi type
III space-time we present the model Universe containing strange quark matter
which is expanding, anisotropic, with a sign of dark energy that help in
accelerated expansion of this Universe. It is also seen that the model Universe
contains both particles and strings but ultimately will have fluid containing
particles only. This model which we consider here is acceptable in view of the
present observations of the Universe. Some physical and geometrical properties
are also discussed.

Abstract:
We use a perturbative method to evaluate the effective action of a free scalar field propagating in the Bianchi type I spacetime with large space anisotropy. The zeta- function regularization method is used to evaluate the action to the second order in the Schwinger perturbative formula. As the quantum corrections contain fourth derivative in the metric we apply the method of iterative reduction to reduce it to the second-order form to obtain the self-consistent solution of the semiclassical gravity theory, The reduced Einstein equation shows that the space anisotropy, which will be smoothed out during the evolution of universe, may play an important role in the dynamics of early universe. We quantize the corresponding minisuperspace model to investigate the behavior of the space anisotropy in the initial epoch. From the wavefunction of the Wheeler-DeWitt equation we see that the probability for the Bianchi type I spacetime with large anisotropy is less then that with a small anisotropy.

Abstract:
Considering the theory of induced gravity coupled to matter fields, taking the $\phi ^6$ interaction potential model we evaluate the one-loop effective potential in a (3+1)dimensional Bianchi type-I spacetime. It is proved that the $\phi ^6$ theory can be regularised in (3+1)dimensional curved spacetime. We evaluate the finite temperature effective potential and study the temperature dependence of phase transitions. The nature of phase transitions in the early universe is clarified to be of first order. The effects of spacetime curvature and arbitrary field coupling on the phase transitions in the early universe are also discussed.

Abstract:
We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant $\Lambda$. The role of viscous fluid and $\Lambda$ term in the evolution the BI space-time is studied. Though the viscosity cannot remove the cosmological singularity, it plays a crucial part in the formation of a qualitatively new behavior of the solutions near singularity. It is shown that the introduction of the $\Lambda$ term can be handy in the elimination of the cosmological singularity. In particular, in case of a bulk viscosity, it provides an everlasting process of evolution ($\Lambda < 0$), whereas, for some positive values of $\Lambda$ and the bulk viscosity being inverse proportional to the expansion, the BI Universe admits a singularity-free oscillatory mode of expansion. In case of a constant bulk viscosity and share viscosity being proportional to expansion, the model allows oscillatory mode accompanied by an exponential growth even with a negative $\Lambda$. Space-time singularity in this case occurs at $t \to -\infty$.