Dynamics of the chiral phase transition at finite chemical potential
We study the dynamics of the chiral phase transition at finite chemical potential in the Gross-Neveu model in the leading order in large-N approximation. We consider evolutions starting in local thermal and chemical equilibrium in the massless unbroken phase for conditions pertaining to traversing a first or second order phase transition. We assume boost invariant kinematics and determine the evolution of the order parameter σ, the energy density and pressure as well as the effective temperature, chemical potential and interpolating number densities as a function of τ.

title: Reheating the postinflationary universe
abstract: We consider the non-equilibrium evolution of the inflaton field coupled to both lighter scalars and fermions. The dissipational dynamics of this field is studied and found to be quite different than that believed in inflationary models. In particular, the damping time scale for the expectation value of the zero momentum mode of the inflaton can be much shorter than that given by the single particle decay rate when the inflaton amplitudes are large, as in chaotic inflation scenarios. We find that the reheating temperature may depart considerably from the usual estimates.

title: Preheating in FRW Universes
abstract: The nonlinear time evolution of the quantum fields is studied in the O(N) model for large N in a radiation dominated FRW universe, with a view towards the phenomenon of explosive particle production due to either spinodal instabilities or parametric amplification, i.e. preheating. Quantum backreaction effects due to the produced particles are included consistently within the large N approximation. We find that preheating persists when the expansion is included, although the amount of particle production is reduced compared to the values found in Minkowski space. We also see that the behavior of the evolving zero mode is very different from that in Minkowski space, though the late time behavior in all cases is determined by a sum rule that implies the existence of Goldstone bosons in the final state.

title: Quantum fluctuations of axions
abstract: We study the time evolution of the quantum fluctuations of the axion field for both the QCD axion as well as axions arising in the context of supergravity and string theories. We explicitly keep track not only of the coherently oscillating zero momentum mode of the axion but also of the higher non-zero momentum modes using the full axion potential. The full axion potential makes possible two kinds of instabilities: spinodal instabilities and parametric resonance instabilities. The presence of either of these instabilities can lead to a quasi-exponential increase in the occupation of non-zero momentum modes and the build-up of the quantum fluctuations of the axions. If either of these becomes a significant effect then axions would no longer be a suitable cold dark matter candidate. Our results confirm the conventional wisdom that these effects are not significant in the setting of an expanding FRW universe and hence axions are indeed cold dark matter candidates.

title: Equilibrium and nonequilibrium properties associated with the chiral phase transition at finite density in the Gross-Neveu model
abstract: We study the dynamics of the chiral phase transition at finite density in the Gross-Neveu (GN) model in the leading order in the large-N approximation. The phase structure of the GN model in this approximation has the property that there is a tricritical point at a fixed temperature and chemical potential separating regions where the chiral transition is first order from that where it is second order. We consider evolutions starting in local thermal and chemical equilibrium in the massless unbroken phase for conditions pertaining to traversing a first or second order phase transition. We assume boost invariant kinematics and determine the evolution of the order parameter \ensuremath{\sigma}, the energy density and pressure as well as the effective temperature, chemical potential and interpolating number densities as a function of the proper time \ensuremath{\tau}. We find that before the phase transition, the system behaves as if it were an ideal fluid in local thermal equilibrium with equation of state $p=\ensuremath{\epsilon}.$ After the phase transition, the system quickly reaches its true broken symmetry vacuum value for the fermion mass and for the energy density. The single particle distribution functions for fermions and antifermions go far out of equilibrium as soon as the plasma traverses the chiral phase transition. We have also determined the spatial dependence of the ``pion'' Green's function $〈\overline{\ensuremath{\psi}}(x){\ensuremath{\gamma}}_{5}\ensuremath{\psi}(x)\overline{\ensuremath{\psi}}(0){\ensuremath{\gamma}}_{5}\ensuremath{\psi}(0)〉$ as a function of the proper time.

title: Dissipation via particle production in scalar field theories.
abstract: We study the nonequilibrium evolution of the expectation value of a scalar field in the broken and unbroken symmetry cases. We find that the particles produced by parametric amplification give rise to dissipative behavior for this mode. However, a {Gamma} {center_dot}{phi} type of term {ital cannot} account for the dissipational dynamics. We are able to show clearly that perturbation theory breaks down at late times, so that dissipation in field theories can only be understood nonperturbatively. When Goldstone bosons are present we find infrared divergences that require a nonperturbative resummation to describe the long-time dynamics. We use the Hartree factorization and the large {ital N} approximation to the O({ital N}) linear {sigma} model to numerically as well as analytically understand the long-time behavior of the zero mode as well as that of the produced particles. The O({ital N}) model case is extremely interesting since, in the spontaneously broken case, the radial mode dissipates all of its energy into production of long-wavelength Goldstone modes. The minima of the effective action (determined by the final value of the expectation value of the scalar field) depend on the initial conditions.

title: Quantum corrections to screening at strong coupling
abstract: We compute a certain class of corrections to (specific) screening lengths in strongly coupled non-abelian plasmas using the AdS/CFT correspondence. In this holographic framework, these corrections arise from various higher curvature interactions modifying the leading Einstein gravity action. The changes in the screening lengths are perturbative in inverse powers of the `t Hooft coupling or of the number of colors, as can be made precise in the context where the dual gauge theory is superconformal. We also compare the results of these holographic calculations to lattice results for the analogous screening lengths in QCD. In particular, we apply these results within the program of making quantitative comparisons between the strongly coupled quark-gluon plasma and holographic descriptions of conformal field theory.

title: On phases of generic toric singularities
abstract: We systematically study the phases of generic toric singularities, using methods initiated in . These correspond to large volume limits of certain Gauged Linear Sigma Models. We show that complete information about the classical regimes of generic U(1)r GLSMs can be obtained by studying the GLSM Lagrangian, appropriately modified in the different phases of the theory. We use this to study some aspects of La,b,c spaces and their non-supersymmetric counterparts.

title: A New Class of Bianchi Type-I Cosmological Models in Scalar-Tensor Theory of Gravitation and Late Time Acceleration
abstract: A new class of a spatially homogeneous and anisotropic Bianchi type-I cosmological models of the universe for perfect fluid distribution within the framework of scalar-tensor theory of gravitation proposed by Sáez and Ballester ( 1986) is investigated. To prevail the deterministic solutions we choose the different scale factors which yield time-dependent deceleration parameters (DP) representing models which generate a transition of the universe from the early decelerated phase to the recent accelerating phase. Three different physically viable models of the universe are obtained in which their anisotropic solutions may enter to some isotropic inflationary era. The modified Einstein’s field equations are solved exactly and the models are found to be in good concordance with recent observations. Some physical and geometric properties of the models are also discussed.