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We study the phase transition from quark-gluon plasma to hadrons in the early universe in the context of non-equilibrium thermodynamics. According to the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electro-weak transition has occurred when the universe was about $1-10\mu s$ old. We focus attention on such a phase transition in the presence of a viscous relativistic cosmological background fluid in the framework of non-detailed balance Ho\v{r}ava-Lifshitz cosmology within an effective model of QCD. We consider a flat Friedmann-Robertson-Walker Universe filled with a non-causal and causal bulk viscous cosmological fluid respectively and investigate the effects of the running coupling constants of Ho\v{r}ava-Lifshitz gravity, $\lambda$, on the evolution of the physical quantities relevant to a description of the early universe, namely, the temperature $T$, scale factor $a$, deceleration parameter $q$ and dimensionless ratio of the bulk viscosity coefficient to entropy density $\frac{\xi}{s}$. We assume that the bulk viscosity cosmological background fluid obeys the evolution equation of the steady truncated (Eckart) and full version of the Israel-Stewart fluid, respectively., Comment: 21 pages, 16 figures

In this paper we study the speed of gravitational waves in a brane world scenario and show that if the extra dimension is space-like, the speed of the propagation of such waves is greater in the bulk than that on the brane. Therefore, the 4D Lorentz invariance is broken in the gravitational sector. A comparison is also made between the red shift of such waves and those of the electromagnetic waves on the brane. Such a comparison is essential for extracting the signature of the extra dimension and thus clarifying the question of maximal velocity of gravitational waves in the bulk., Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:gr-qc/0702103; and text overlap with arXiv:arXiv:gr-qc/0305041 by other author

We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies. We present an ansatz for the initial conditions which leads to a unique determination of the expansion coefficients in the construction of the wave packets with probability distributions which, in an interesting contrast to some of the earlier works, agree well with all possible classical paths. The possible relationship between these initial conditions and signature transition in the context of classical cosmology is also discussed., Comment: 12 pages, 12 eps figures, to appear in Phys. Lett. A

We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this context we show that a local change of the preferred conformal frame results in a Hamilton-Jacobi equation describing a particle with adjustable mass. In this equation the dynamical characteristics of the particle substantially depends on the applied conformal factor and local geometry. Relevant interpretations of the results are also discussed.

We offer a pragmatic approach for constructing radiating-pointmultipole solutions to Maxwell's equations in a class of cosmological backgrounds, from the Hertzian oscillator solution. We suggest that the derivation of the latter in terms of differential forms offers certain computational advantages as well as suggesting Lie differentiation of solutions as a natural method to generate new solutions in space-times with isometries. We explicitly demonstrate these ideas by constructing the flux of instantaneous electromagnetic radiation from a harmonic quadrupole in a Robertson-Walker space-time containing flat spatial universes.

We consider a brane world scenario in which the bulk action is assumed to have the form of a generic function of the Ricci scalar f(R) and derive the resulting Einstein field equation on the brane. In a constant curvature bulk a conserved geometric quantity appears in the field equations which can be associated with matter. We present spherically symmetric solutions which account for galaxy rotation curves in a specific form. Then cosmological solutions by assuming a specific form for f(R) are derived which can explain an accelerated expanding universe.

We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a ``canonical initial slope" for a given initial wave function, which optimizes some desirable properties of the resulting wave packet, most importantly good classical-quantum correspondence. This can be properly denoted as a canonical wave packet. We introduce a general method for finding these canonical initial slopes which is generalization of our earlier work., 19 pages, 8 figures

Motivated by the Randall-Sundrum brane-world scenario, we discuss the classical and quantum dynamics of a (d+1)-dimensional boundary wall between a pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general -- but not completely arbitrary -- matter fields living on the boundary ``brane universe'' and its geometry is that of an Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The effective action governing the model in the mini-superspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semi-classical level; these correspond to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semi-classical level, and we consider the possible localization of the brane universe's wavefunction away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections., Shortened to match version accepted by Phys. Rev. D (unabridged text found in version 2), 42 pages, 9 figures, Rextex4

We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by establishing certain `moving' jump conditions across them. We show how a first integral of the differential equations, if available, can also be used for checking the accuracy of the numerical solution., 9 pages, 7 eps figures, to appear in Comput. Phys. Com

We analyse a classical model of gravitation coupled to a self interacting scalar field. We show that, within the context of this model for Robertson-Walker cosmologies, there exist solutions in the spatially non-flat cases exhibiting transitions from a Euclidean to a Lorentzian spacetime. We then discuss the conditions under which these signature changing solutions to Einstein's field equations exist. In particular, we find that an upper bound for the cosmological constant exists and that close to the signature changing hypersurface, both the scale factor and the scalar field have to be constant. Moreover we find that the signature changing solutions do not exist when the scalar field is massless., 9 pages plus 4 postscript figures. To appear in the Int. J. Mod. Phys. A

A variant of the divergence theory for vacuum-condensation developed in a previous communication is analyzed from the viewpoint of a 'time' asymmetric law in vacuum. This law is found to establish a substantial distinction between dynamically allowed vacuum-configurations related by signature changing duality transformations., 6 pages, latex file