Quantum fluctuations of axions
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: Non-Abelian soft boson phase transitions and large-scale structure.
abstract: A new class of models with Pseudo-Nambu-Goldstone bosons (PNGB`s) is constructed using a non-Abelian symmetry in the right handed Majorana neutrino sector of see-saw neutrino mass models. The phase structure of these models is examined both at zero and non-zero temperatures, with particular emphasis on their phase transition characteristics. We find that the vacuum manifold of these models exhibits a rich structure in terms of possible topological defects, and we argue that these models may have applications to late time phase transition theories of structure formation.

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: 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: 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: 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: Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter
abstract: The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra’s manifold by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law type. Using these two forms, Einstein’s modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier,  2414 (1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component $\sigma^{1}_{~1}$ of the shear tensor $\sigma^{j}_{~i}$. This condition leads to A=(BC)m, where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.

title: Multipoint correlators of conformal field theories: implications for quantum critical transport
abstract: We compute three-point correlators between the stress-energy tensor and con- served currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then do the computation using holography. In the holographic approach, the correlators are computed from an e↵ective action on 3+1 dimensional anti-de Sitter space (AdS4), and depend upon the co-ecient, , of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus fixing the values of . The CFTs of free fermions and bosons take the values =1 /12,1/12 respectively, and so saturate the bound | | 1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of . The value of also controls the fre- quency dependence of the conductivity, and other properties of quantum-critical transport at non-zero temperatures. Our results for the values of lead to an appealing physical inter- pretation of particle-like or vortex-like transport near quantum phase transitions of interest in condensed matter physics. This paper includes appendices reviewing key features of the AdS/CFT correspondence for condensed matter physicists.

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: 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.