We investigate the generality of inflation (the probability of inflation, in other words) in closed Friedmann-Robertson-Walker models for a wide class of quintessence potentials. It is shown that inflation is not suppressed for most of them for a wide range of their parameters. This allows us to decide if inflation is common even in the case of a closed universe.

In the large $N_c$ limit, the mass spectrum of the $L=1\mathrm{}$ orbitally excited baryons $N^{*}$ has a very simple structure, with states degenerate in pairs of spins $J=(\frac{1}{2},\frac{3}{2}),(\frac{3}{2},\frac{5}{2}),$ corresponding to irreducible representations (towers) of the contracted ${\mathrm{SU}\left(4\right)\mathrm{}}_c$ symmetry group. The mixing angles are completely determined in this limit. Using a mass operator approach, we study ${1/N}_c$ corrections to this picture, pointing out a fourfold ambiguity in the correspondence of the observed baryons with the large $N_c$ states. For each of the four possible assignments, we fit the coefficients of the quark operators contributing to the mass spectrum to ${O(N}_c^{-1}).\mathrm{}$ We comment on the implications of our results for the constituent quark model description of these states.

We analyze excited baryon properties via a ${1/N}_c$ expansion from two perspectives: as resonances in meson-nucleon scattering, and as single-quark excitations in the context of a simple quark model. For both types of analysis one can derive novel patterns of degeneracy that emerge as $N_c\to \infty ,$ and that are shown to be compatible with one another. This helps justify the single-quark excitation picture and may give some insight into its successes. We also find that in the large $N_c$ limit one of the $S_{11}$ baryons does not couple to the $\pi -N$ channel but couples to the $\eta -N$ channel. This is empirically observed in the $N\left(1535\right),$ which couples very weakly to the $\pi -N$ channel and quite strongly to the $\eta -N$ channel. The comparatively strong coupling of the $N\left(1650\right)\mathrm{}$ to the $\pi -N$ channel and weak coupling to $\eta -N$ channel is also predicted. In the context of the simple quark model picture we reproduce expressions for mixing angles that are accurate up to ${O(1/N}_c)$ corrections and are in good agreement with mixing angles extracted phenomenologically.

We investigate the dynamics of the Papapetrou equations in Kerr spacetime. These equations provide a model for the motion of a relativistic spinning test particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter space search for signs of chaotic dynamics by calculating the Lyapunov exponents for a large variety of initial conditions. We find that the Papapetrou equations admit many chaotic solutions, with the strongest chaos occurring in the case of eccentric orbits with pericenters close to the limit of stability against plunge into a maximally spinning Kerr black hole. Despite the presence of these chaotic solutions, we show that physically realistic solutions to the Papapetrou equations are not chaotic; in all cases, the chaotic solutions either do not correspond to realistic astrophysical systems, or involve a breakdown of the test-particle approximation leading to the Papapetrou equations (or both). As a result, the gravitational radiation from bodies spiraling into much more massive black holes (as detectable, for example, by LISA, the Laser Interferometer Space Antenna) should not exhibit any signs of chaos.

The determination of the shower development in air using fluorescence yield is subject to corrections due to the angular spread of the particles in the shower. This could introduce systematic errors in the energy determination of an extensive air shower through the fluorescence technique.

In light of a recent study on the dark energy models that manifest an equation of state $w<\mathrm{}-1,$ we investigate the cosmological evolution of a phantom field in a specific potential, exponential potential in this paper. The phase plane analysis shows that the there is a late time attractor solution in this model, which addresses similar issues to that of fine-tuning problems in conventional quintessence models. The evolution of the state w is determined by the attractor solution which is dependent on the $\lambda$ parameter in the potential. We also show that this model is stable for our present observable universe.

We calculate the thermal partition function in the canonical ensemble for type IIB superstrings in the plane wave background with a constant null RR five-form. The Hagedorn temperature is found to be higher than the corresponding value for strings in flat space. In the limit corresponding to the weakly coupled field theory we find that the Hagedorn temperature is pushed to infinity. The key property of strings in the plane wave background under investigation on which our result relies is that the effective mass of the bosonic and fermionic coordinates in the light-cone gauge is proportional to the momentum $p^{+}.$ The free energy is finite as the Hagedorn temperature is approached from below, suggesting a possible phase transition.

The partition function with ring diagrams at finite temperature is exactly calculated by using contour integrals in the complex energy plane. It contains a pole part with a temperature- and momentum-dependent mass and a phase shift part induced by the off-shell effect in a hot medium. The thermodynamic potentials for the ${\phi }^4$ and ${\phi }^3$ interactions are calculated and compared with the quasiparticle (pole) approximation. It is found that the off-shell effect on the equation of state is remarkable.

We use the matrix model to describe the $\mathcal{N}=2\mathrm{}$ $\mathrm{SO}\left(N\right)/Sp\left(N\right)\mathrm{}$ supersymmetric gauge theories with massive hypermultiplets in the fundamental representation. By taking the tree level superpotential perturbation made of a polynomial of a scalar chiral multiplet, the effective action for the eigenvalues of the chiral multiplet can be obtained. A loop equation is obtained by varying this action with respect to an eigenvalue. By analyzing this equation, we derive the Seiberg-Witten curve within the context of the matrix model.

Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric ${\phi }^4$ kinks exhibits the following. (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the nonanomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and nonanomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a ${\Phi }^4$ model in $1+1$ dimensions with a symmetric and a double well potential. We use the two-particle point-irreducible (2PPI) formalism and go beyond the Hartree approximation by including the sunset term. In addition to the mean field $\phi \mathrm{}\left(t\right)=〈\Phi 〉$ the 2PPI formalism uses as a variational parameter a time dependent mass ${\mathcal{M}}^2\mathrm{}\left(t\right)\mathrm{}$ which contains all local insertions into the Green’s function. We compare our results to those obtained in the Hartree approximation. In the symmetric ${\Phi }^4$ theory we observe that the mean field shows a stronger dissipation than the one found in the Hartree approximation. The dissipation is roughly exponential in an intermediate time region. In the theory with spontaneous symmetry breaking, i.e., with a double well potential, the field amplitude tends to zero, i.e., to the symmetric configuration. This is expected on general grounds: in $\mathrm{}(1+1)\mathrm{}$-dimensional quantum field theory there is no spontaneous symmetry breaking for $T>\mathrm{}0,$ and so there should be none at finite energy density (microcanonical ensemble), either. Within the time range of our simulations the momentum spectra do not thermalize and display parametric resonance bands.

We consider a cosmological brane moving in a static five-dimensional bulk spacetime endowed with a scalar field whose potential is exponential. After studying various cosmological behaviors for the homogeneous background, we investigate the fluctuations of the brane that leave spacetime unaffected. A single mode embodies these fluctuations and obeys a wave equation which we study for bouncing and ever-expanding branes.

We investigate both analytically and numerically the evolution of scalar perturbations generated in models which exhibit a smooth transition from a contracting to an expanding Friedmann universe. If the perturbation equations are formulated as second order equations for either the Bardeen potential $\Psi$ or the curvature perturbation on uniform comoving hypersurfaces $\zeta ,$ at best one of them can stay regular during the transition. We find that the resulting spectral index in the late radiation dominated universe depends on which of these two variables passes regularly through the transition. The results can be parametrized by the exponent q defining the rate of contraction of the universe, or equivalently through the equation of state $w=\left(2\mathrm{}-q\right)/3q$ of the background fluid. For $q>~-\frac{1}{2}$ we find that there are no stable cases where both $\Psi$ and $\zeta$ are regular during the transition. In particular, for $0<q\ll 1,$ we find that the resulting spectral index is close to scale invariant if $\Psi$ is regular, whereas it has a steep blue behavior if $\zeta$ is regular. We also show that as long as $q<~1$ and we are in the regime where corrections can be ignored, perturbations remain small during contraction in the sense that there exists a gauge in which all the metric and matter perturbation variables are small. This work has important implications for the current debate concerning the nature of perturbations evolving through a collapsing regime into an expanding one: it shows that if in the ekpyrotic model, where $0<q\ll 1,$ the Bardeen potential passes regularly through the transition, this leads to a nearly scale invariant spectrum with $n=1\mathrm{}-2q,$ whereas in the case of dilaton-driven string cosmology we have the opposite situation. There it is assumed that $\zeta$ passes regularly through the transition, leading to a very blue spectrum of highly suppressed perturbations.

We propose an alternative implementation of the curvaton mechanism for generating the curvature perturbations which does not rely on a late decaying scalar decoupled from inflation dynamics. In our mechanism the supersymmetric Higgs scalars are coupled to the inflaton in a hybrid inflation model, and this allows the conversion of the isocurvature perturbations of the Higgs fields to the observed curvature perturbations responsible for large scale structure to take place during reheating. We discuss an explicit model which realizes this mechanism in which the $\mu$ term in the Higgs superpotential is generated after inflation by the vacuum expectation value of a singlet field. The main prediction of the model is that the spectral index should deviate significantly from unity, $|n-1|\sim \mathrm{0.1.}$ We also expect relic isocurvature perturbations in neutralinos and baryons, but no significant departures from Gaussianity and no observable effects of gravity waves in the CMB spectrum.

Entropy production by dilaton decay is studied in the model where the dilaton acquires a potential via gaugino condensation in the hidden gauge group. Its effect on Affleck-Dine baryogenesis is investigated with and without nonrenormalizable terms in the potential. It is shown that the baryon asymmetry produced by this mechanism with higher-dimensional terms is diluted by the dilaton decay and can be regulated to the observed value.

We clarify the quantitative nature of the cosmological evolution of a global string network, that is, the energy density, peculiar velocity, velocity squared, Lorentz factor, formation rate of loops, and emission rate of Nambu-Goldstone bosons, based on a new type of numerical simulation of scalar fields in Eulerian meshes. We give a detailed explanation of a method to extract the above-mentioned quantities to characterize string evolution by analyzing scalar fields in Eulerian meshes from a Lagrangian viewpoint. We confirm our previous claim that the number of long strings per horizon volume in a global string network is smaller than in the case of a local string network by a factor of $\sim 10$ even under cosmological situations, and its reason is clarified.

In this paper we study the cosmological dynamics of Randall-Sundrum braneworld type scenarios in which the five-dimensional Weyl tensor has a nonvanishing projection onto the three-brane where matter fields are confined. Using dynamical systems techniques, we study how the state space of Friedmann-Lemaître-Robertson-Walker (FLRW) and Bianchi type I scalar field models with an exponential potential is affected by the bulk Weyl tensor, focusing on the differences that appear with respect to standard general relativity and also Randall-Sundrum cosmological scenarios without the Weyl tensor contribution.

We present methods to compute maps of cosmic microwave background fluctuations from high resolution cosmic string networks using a full Boltzmann code, on both large and small angular scales. The accuracy and efficiency of these methods are discussed.

We study gravitational lensing by the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole of heterotic string theory and obtain the angular position and magnification of the relativistic images. Modeling the supermassive central object of the galaxy as a GMGHS black hole, we estimate the numerical values of different strong-lensing parameters. We find that there is no significant string effect present in the lensing observables in the strong-gravity scenario.