Acceleration and Deceleration in Curvature Induced Phantom Model of the Late and Future Universe, Cosmic Collapse as Well as its Quantum Escape

Here, cosmology of the late and future universe is obtained from $f(R)$-gravity with non-linear curvature terms $R^2$ and $R^3$ ($R$ being the Ricci scalar curvature). It is different from $f(R)$-dark enrgy models, where non-linear curvature terms are taken as gravitational alternative of dark energy. In the present model, neither linear nor no-linear curvature terms are taken as dark energy. Rather, dark energy terms are induced by curvature terms in the Friedmann equation derived from $f(R)$-gravitational equations. It has advantage over $f(R)$- dark energy models in the sense that the present model satisfies WMAP results and expands as $\sim t^{2/3}$ during matter-dominance. So, it does not have problems due to which $f(R)$-dark energy models are criticized. Curvature-induced dark energy, obtained here, mimics phantom. Different phases of this model, including acceleration and deceleration during phantom phase, are investigated here.It is found that expansion of the universe will stop at the age $(3.87 t_0 + 694.4 {\rm kyr})$ ($t_0$ being the present age of the universe) and after this epoch, it will contract and collapse by the time $(336.87 t_0 + 694.4 {\rm kyr})$. Further,it is shown that universe will escape predicted collapse (obtained using classical mechanics) on making quantum gravity corrections relevant near collapse time due to extremely high energy density and large curvature analogous to the state of very early universe. Interestingly, cosmological constant is also induced here, which is very small in classical domain, but very high in quantum domain.Comment: 33 page

Light-Front QCD in Light-Cone Gauge

The light-front (LF) quantization of QCD in light-cone (l.c.) gauge is discussed. The Dirac method is employed to construct the LF Hamiltonian and theory quantized canonically. The Dyson-Wick perturbation theory expansion based on LF-time ordering is constructed. The framework incorporates in it simultaneously the Lorentz gauge condition as an operator equation as well. The propagator of the dynamical $\psi_+$ part of the free fermionic propagator is shown to be causal while the gauge field propagator is found to be transverse. The interaction Hamiltonian is re-expressed in the form closely resembling the one in covariant theory, except for additional instantaneous interactions, which can be treated systematically. Some explicit computations in QCD are given.Comment: Presented at VII Hadron Physics 2000, Caraguatatuba, Sao Paulo, Brazil, 10-15 April 200

Light-Front-Quantized QCD in Covariant Gauge

The light-front (LF) canonical quantization of quantum chromodynamics in covariant gauge is discussed. The Dirac procedure is used to eliminate the constraints in the gauge-fixed front form theory quantum action and to construct the LF Hamiltonian formulation. The physical degrees of freedom emerge naturally. The propagator of the dynamical $\psi_+$ part of the free fermionic propagator in the LF quantized field theory is shown to be causal and not to contain instantaneous terms. Since the relevant propagators in the covariant gauge formulation are causal, rotational invariance---including the Coulomb potential in the static limit---can be recovered, avoiding the difficulties encountered in light-cone gauge. The Wick rotation may also be performed allowing the conversion of momentum space integrals into Euclidean space forms. Some explicit computations are done in quantum electrodynamics to illustrate the equivalence of front form theory with the conventional covariant formulation. LF quantization thus provides a consistent formulation of gauge theory, despite the fact that the hyperplanes $x^{\pm}=0$ used to impose boundary conditions constitute characteristic surfaces of a hyperbolic partial differential equation.Comment: LaTex, 16 page

A Hybrid Model for QCD Deconfining Phase Boundary

Intensive search for a proper and realistic equations of state (EOS) is still continued for studying the phase diagram existing between quark gluon plasma (QGP) and hadron gas (HG) phases. Lattice calculations provide such EOS for the strongly interacting matter at finite temperature ($T$) and vanishing baryon chemical potential ($\mu_{B}$). These calculations are of limited use at finite $\mu_{B}$ due to the appearance of notorious sign problem. In the recent past, we had constructed a hybrid model description for the QGP as well as HG phases where we make use of a new excluded-volume model for HG and a thermodynamically-consistent quasiparticle model for the QGP phase and used them further to get QCD phase boundary and a critical point. Since then many lattice calculations have appeared showing various thermal and transport properties of QCD matter at finite $T$ and $\mu_{B}=0$. We test our hybrid model by reproducing the entire data for strongly interacting matter and predict our results at finite $\mu_{B}$ so that they can be tested in future. Finally we demonstrate the utility of the model in fixing the precise location, the order of the phase transition and the nature of CP existing on the QCD phase diagram. We thus emphasize the suitability of the hybrid model as formulated here in providing a realistic EOS for the strongly interacting matter.Comment: 22 pages, 10 figures. corrected version published in Physical Review D. arXiv admin note: substantial text overlap with arXiv:1201.044