We present a study of inhomogeneous big bang nucleosynthesis with emphasis on transport phenomena. We combine a hydrodynamic treatment to a nuclear reaction network and compute the light element abundances for a range of inhomogeneity parameters. We find that shortly after annihilation of electron-positron pairs, Thomson scattering on background photons prevents the diffusion of the remaining electrons. Protons and multiply charged ions then tend to diffuse into opposite directions so that no net charge is carried. Ions with $Z>\mathrm{}1\mathrm{}$ get enriched in the overdense regions, while protons diffuse out into regions of lower density. This leads to a second burst of nucleosynthesis in the overdense regions at $T<\mathrm{}20\mathrm{}\hspace{0.5em}\mathrm{keV},$ leading to enhanced destruction of deuterium and lithium. We find a region in the parameter space at $2.1\times {10}^{-10}<\eta <5.2\mathrm{}\times {10}^{-10}$ where constraints ${}^7\mathrm{Li}/\mathrm{H}<{10}^{-9.7}$ and $\mathrm{D}/\mathrm{H}<{10}^{-4.4}$ are satisfied simultaneously.

We consider the fate of the observable universe in the light of the discovery of a dark energy component to the cosmic energy budget. We extend results for a cosmological constant to a general dark energy component and examine the constraints on phenomena that may prevent the eternal acceleration of our patch of the universe. We find that the period of accelerated cosmic expansion has not lasted long enough for observations to confirm that we are undergoing inflation; such an observation will be possible when the dark energy density has risen to between 90% and 95% of the critical. The best we can do is make cosmological observations in order to verify the continued presence of dark energy to some high redshift. Having done that, the only possibility that could spoil the conclusion that we are inflating would be the existence of a disturbance (the surface of a true vacuum bubble, for example) that is moving toward us with sufficiently high velocity, but is too far away to be currently observable. Such a disturbance would have to move toward us with speed greater than about $0.8c$ in order to spoil the late-time inflation of our patch of the universe and yet avoid being detectable.

Numerical solutions to the nonlinear sigma model, a wave map from $3+1$ Minkowski space to $S^3,$ are computed in three spatial dimensions using adaptive mesh refinement. For initial data with compact support the model is known to have two regimes: one in which regular initial data forms a singularity and another in which the energy is dispersed to infinity. The transition between these regimes has been shown in spherical symmetry to demonstrate threshold behavior similar to that between black hole formation and dispersal in gravitating theories. Here, I generalize the result by removing the assumption of spherical symmetry. The evolutions suggest that the spherically symmetric critical solution remains an intermediate attractor separating the two end states.

An analysis of supersymmetric dark matter under the Yukawa unification constraint is given. The analysis utilizes the recently discovered region of the parameter space of models with gaugino mass nonuniversalities where large negative supersymmetric corrections to the b quark mass appear to allow $b-\tau$ unification for a positive $\mu$ sign consistent with the $\overrightarrow{b}s+\gamma$ and $g_{\mu }-2$ constraints. In the present analysis we use the revised theoretical determination of $a_{\mu }^{\mathrm{SM}}$ $\left[a_{\mu }{=(g}_{\mu }-2\right)/2]$ in computing the difference $a_{\mu }^{\mathrm{expt}}-a_{\mu }^{\mathrm{SM}}$ which takes into account a reevaluation of the light by light contribution, which has a positive sign. The analysis shows that the region of parameter space with nonuniversalities of the gaugino masses that allows for unification of Yukawa couplings also contains regions that allow the satisfaction of the relic density constraint. Specifically, we find that the lightest neutralino mass consistent with the relic density constraint, $b\tau$ unification for SU(5), and $b-t-\tau$ unification for SO(10), in addition to other constraints, lies in the region below 80 GeV. An analysis of the maximum and the minimum neutralino-proton scalar cross sections for the allowed parameter space, including the effect of a new determination of the pion-nucleon sigma term, is also given. It is found that the full parameter space for this class of models can be explored in the next generation of proposed dark matter detectors.

In crystalline color superconductivity, quark pairs form at nonzero total momentum. This crystalline order potentially enlarges the domain of color superconductivity in cold dense quark matter. We present a perturbative calculation of the parameters governing the crystalline phase and show that this is indeed the case. Nevertheless, the enhancement is modest, and to lowest order is independent of the strength of the color interaction.

We derive the nonequilibrium real-time evolution of an $O\left(N\right)\mathrm{}$-invariant scalar quantum field theory in the presence of a nonvanishing expectation value of the quantum field. Using a systematic $1/N$ expansion of the 2PI effective action to next-to-leading order, we obtain nonperturbative evolution equations which include scattering and memory effects. The equivalence of the direct method, which requires the resummation of an infinite number of skeleton diagrams, with the auxiliary-field formalism, which involves only one diagram at next-to-leading order, is shown.

The bound state spectrum of the massive Thirring model is studied in the framework of the canonical quantization in the rest frame. First, we quantize the field with the massless free fermion basis states. Then, we make a Bogoliubov transformation. This leads to the natural mass renormalization. The bound state spectrum is analytically solved by the $q\overline{q}$ Fock space. It is found that the spectrum has the right behavior both for the weak and for the strong coupling limits after the appropriate wave function regularization. This regularization is quite clear and the treatment is self-consistent for the bound state problem compared to other regularizations. Further, we show that the interaction between $q\overline{q}$ bosons is always repulsive and therefore there is no bound state in the four fermion $\left(qq\overline{q}\overline{q}\right)$ Fock space. This confirms that there is only one bound state in the massive Thirring model.

The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors $N_c^{\mathrm{thr}},$ dividing the theories with essentially different dynamics, is established. For the number of colors $N_c\ll N_c^{\mathrm{thr}},$ an anisotropic dynamics of confinement with the confinement scale much less than ${\Lambda }_{\mathrm{QCD}}$ and a rich spectrum of light glueballs is realized. For $N_c$ of order $N_c^{\mathrm{thr}}$ or larger, a conventional confinement dynamics takes place. It is found that the threshold value $N_c^{\mathrm{thr}}$ grows rapidly with the magnetic field $[N_c^{\mathrm{thr}}\gtrsim 100$ for $|\mathrm{eB}|\gtrsim \left(1\mathrm{}\mathrm{GeV}{)}^2\right].$ In contrast with QCD with a nonzero baryon density, there are no principal obstacles for examining these results and predictions in lattice computer simulations.

We show how to compute transport coefficients in gauge theories by considering the expansion of the Kubo formulas in terms of ladder diagrams in the imaginary time formalism. All summations over Matsubara frequencies are performed and the analytical continuation to get the retarded correlators is done. As an illustration of the procedure, we present a derivation of the transport equation for the shear viscosity in the scalar theory. Assuming the hard thermal loop approximation for the screening of distant collisions of the hard particles in the plasma, we derive two integral equations for the effective vertices which, to logarithmic accuracy, are shown to be identical to the linearized Boltzmann equations previously found by Arnold, Moore, and Yaffe.

The problem of the interpretation of the ${ħ}^0$-order part of radiative corrections to the effective gravitational field is considered. It is shown that variations of the Feynman parameter in gauge conditions fixing the general covariance are equivalent to spacetime diffeomorphisms. This result is proved for arbitrary gauge conditions at the one-loop order. It implies that the gravitational radiative corrections of the order ${ħ}^0$ to the spacetime metric can be physically interpreted in a purely classical manner. As an example, the effective gravitational field of a black hole is calculated in the first post-Newtonian approximation, and the secular precession of a test particle orbit in this field is determined.

We study eccentric equatorial orbits of a test-body around a Kerr black hole under the influence of gravitational radiation reaction. We have adopted a well established two-step approach: assuming that the particle is moving along a geodesic (justifiable as long as the orbital evolution is adiabatic) we calculate numerically the fluxes of energy and angular momentum radiated to infinity and to the black hole horizon, via the Teukolsky-Sasaki-Nakamura formalism. We can then infer the rate of change of orbital energy and angular momentum and thus the evolution of the orbit. The orbits are fully described by a semilatus rectum p and an eccentricity e. We find that while, during the inspiral, e decreases until shortly before the orbit reaches the separatrix of stable bound orbits [which is defined by $p_s\mathrm{}\left(e\right)],$ in many astrophysically relevant cases the eccentricity will still be significant in the last stages of the inspiral. In addition, when a critical value $p_{\mathrm{crit}}\mathrm{}\left(e\right)\mathrm{}$ is reached, the eccentricity begins to increase as a result of continued radiation induced inspiral. The two values $p_s,$$\hspace{0.5em}{p}_{\mathrm{crit}}$ (for given $e)$ move closer to each other, in coordinate terms, as the black hole spin is increased, as they do also for fixed spin and increasing eccentricity. Of particular interest are moderate and high eccentricity orbits around rapidly spinning black holes, with $p\left(e\right)\mathrm{}\approx p_s\mathrm{}\left(e\right).$ We call these “zoom-whirl” orbits, because of their characteristic behavior involving several revolutions around the central body near periastron. Gravitational waveforms produced by such orbits are calculated and shown to have a very particular signature. Such signals may well prove of considerable astrophysical importance for the future Laser Interferometer Space Antenna detector.

We calculate the bispectrum of the gravitational field fluctuations generated during warm inflation, where dissipation of the vacuum potential during inflation is the mechanism for structure formation. The bispectrum is nonzero because of the self-interaction of the scalar field. We compare the predictions with those of standard, or “supercooled,” inflationary models, and consider the detectability of these levels of non-Gaussianity in the bispectrum of the cosmic microwave background. We find that the levels of non-Gaussianity for warm and supercooled inflation are comparable, and overridden by the contribution to the bispectrum due to other physical effects. We also conclude that the resulting bispectrum values will be undetectable in the cosmic microwave background for both the MAP and Planck Surveyor satellites.

If the graviton possesses an arbitrarily small (but nonvanishing) mass, perturbation theory implies that cosmic strings have a nonzero Newtonian potential. Nevertheless in Einstein gravity, where the graviton is strictly massless, the Newtonian potential of a cosmic string vanishes. This discrepancy is an example of the van Dam–Veltman–Zakharov (VDVZ) discontinuity. We present a solution for the metric around a cosmic string in a braneworld theory with a graviton metastable on the brane. This theory possesses those features that yield a VDVZ discontinuity in massive gravity, but nevertheless is generally covariant and classically self-consistent. Although the cosmic string in this theory supports a nontrivial Newtonian potential far from the source, one can recover the Einstein solution in a region near the cosmic string. That latter region grows as the graviton’s effective linewidth vanishes (analogous to a vanishing graviton mass), suggesting the lack of a VDVZ discontinuity in this theory. Moreover, the presence of scale dependent structure in the metric may have consequences for the search for cosmic strings through gravitational lensing techniques.

We present an alternative way to calculate the screening of the static potential between two charges in (non-)Abelian gauge theories at high temperatures. Instead of a loop expansion of a gauge boson self-energy, we evaluate the energy shift of the vacuum to order $e^2$ after applying an external static magnetic field and extract a temperature- and momentum-dependent dielectric permittivity. The hard thermal loop gluon and photon Debye masses are recovered from the lowest lying Landau levels of the perturbed vacuum. In QED, the complete calculation exhibits an interesting cancellation of terms, resulting in a logarithmic running $\alpha \mathrm{}\left(T\right).$ In QCD, a Landau pole in ${\alpha }_s$ arises in the infrared from the sign of the gluon contribution, as in more sophisticated thermal renormalization group calculations.

We study the running of the Lüscher-Weisz-Wolff (LWW) coupling constant in the two-dimensional $O\left(3\right)\mathrm{}$ nonlinear σ model. To investigate the continuum limit we refine the lattice spacing from the $\frac{1}{16}$ value used by LWW up to $\frac{1}{160}.$ We find larger lattice artifacts than those estimated by LWW and that most likely the coupling constant runs slower than predicted by perturbation theory. A precise determination of the running in the continuum limit would require a controlled ansatz of extrapolation, which, we argue, is not presently available.

The low $Q^2$ wave functions of pions and kaons are studied in terms of an expansion in hadron-like Fock state fluctuations. In this formalism, the pion and kaon wave functions are related to one another, allowing us, in principle, to obtain the full parton structure of both pions and kaons from the measurement of light valence quark distributions. We show that the model also predicts the intrinsic sea of pions and kaons needed at the low $Q^2$ scale where perturbative evolution starts. Finally, we analyze the feasibility of a method to extract the kaon’s parton distribution functions within this approach and compare it with available experimental data.

We analyze the forward-backward asymmetry of the decays $\overrightarrow{B}(\pi ,K){\mathcal{l}}^{+}{\mathcal{l}}^{-}$ with $\mathcal{l}=\mu$ or τ in the framework of the constrained minimal supersymmetric standard model. We find that the asymmetry is enhanced at large $\tan \beta$ and depends strongly on the sign of the μ parameter. For $\mu >0,$ the asymmetry is typically large and observable, whereas for $\mu <0\mathrm{}$ it changes the sign and is suppressed by an order of magnitude. Including cosmological constraints we find that the asymmetry has a maximal value of about $30\%,$ produced when Higgs- and gauge-induced flavor violations are of comparable size, at a value of $\tan \beta \simeq 35.$ The present constraints from the B factories are too weak to constrain parameter space, and the regions excluded by them are already disfavored by at least one of $\mathrm{BR}\left(\overrightarrow{B}{X}_s\gamma \right),$ $g-2,$ and/or cosmology. The size of the asymmetry is mainly determined by the flavor of the final state lepton rather than the flavor of the pseudoscalar.

We study the three positivity constraints on the eight virtual photon structure functions, derived from the Cauchy-Schwarz inequality and which are, hence, model independent. The photon structure functions obtained from the simple parton model show quite different behaviors in a massive or a massless quark case, but they satisfy, in both cases, the three positivity constraints. We then discuss an inequality which holds among the unpolarized and polarized photon structure functions $F_1^{\gamma },$ $g_1^{\gamma },$ and $W_{\mathrm{TT}}^{\tau },$ in the kinematic region ${\Lambda }^2\ll P^2\ll Q^2,$ where $-Q^2\left(-P^2\right)$ is the mass squared of the probe (target) photon, and we examine whether this inequality is satisfied by the perturbative QCD results.

The order parameter for the pure Yang-Mills phase transition is the Polyakov loop which encodes the symmetries of the $Z_N$ center of the $\mathrm{SU}\left(N\right)\mathrm{}$ gauge group. On the other side the physical degrees of freedom of any asymptotically free gauge theory are hadronic states. Using the Yang-Mills trace anomaly and the exact $Z_N$ symmetry we construct a model able to communicate to the hadrons the information carried by the order parameter.