In this paper we analyze the asymptotic behavior of Cardassian cosmological models filled with a perfect fluid and a scalar field with an exponential potential. Cardassian cosmologies arise from modifications of the Friedmann equation, and among the different proposals within that framework we will choose those of the form $3H^2-\rho \propto {\rho }^n$ with $n<1$. We construct two three-dimensional dynamical systems arising from the evolution equations, respectively, adapted for studying the high and low energy limits. Using standard dynamical systems techniques we find the fixed points and characterize the solutions they represent. We pay especial attention to the properties inherent to the modifications and compare with the (standard) unmodified scenario. Among other interesting results, we find there are no late-time tracking attractors.

We show how the maximally helicity violating (MHV) scattering amplitudes for gravitons can be related to current correlators and vertex operators in twistor space. This is similar to what happens in Yang-Mills theory and raises the possibility of a direct twistor-string-like construction for $\mathcal{N}=8$ supergravity.

It has recently been suggested that collisions of transversely polarized protons and antiprotons at the GSI could be used to determine the nucleon’s transversity densities from measurements of the double-spin asymmetry for the Drell-Yan process. We analyze the role of higher-order perturbative QCD corrections in this kinematic regime, in terms of the available fixed-order contributions as well as of all-order soft-gluon resummations. We find that the combined perturbative corrections to the individual unpolarized and transversely polarized cross sections are large. We trace these large enhancements to soft-gluon emission near partonic threshold, and we suggest that with a physically motivated cutoff enhancements beyond lowest order are moderated relative to resummed perturbation theory, but still significant. The unpolarized dilepton cross section for the GSI kinematics may therefore provide information on the relation of perturbative and nonperturbative dynamics in hadronic scattering. The spin asymmetry turns out to be rather robust, relatively insensitive to higher orders, resummation, and the cutoffs.

We present results for different observables in weak decays of pseudoscalar and vector mesons with a heavy $c$ or $b$ quark. The calculations are done in a nonrelativistic constituent quark model improved at some instances by heavy quark effective theory constraints. We determine pseudoscalar and vector meson decay constants that within a few percent satisfy $f_V{M}_V/f_P{M}_P=1$, a result expected in heavy quark symmetry when the heavy quark masses tend to infinity. We also analyze the semileptonic $B\to D$ and $B\to D^{*}$ decays for which we evaluate the different form factors. Here we impose heavy quark effective theory constraints among form factors that are not satisfied by a direct quark model calculation. The value of the form factors at zero recoil allows us to determine, by comparison with experimental data, the value of the $|V_{cb}|$ Cabibbo-Kobayashi-Maskawa matrix element. From the $B\to D$ semileptonic decay we get $|V_{cb}|=0.040\pm 0.006$, in perfect agreement with our previous determination based on the study of the semileptonic ${\Lambda }_b\to {\Lambda }_c$ decay and also in excellent agreement with a recent experimental determination by the DELPHI Collaboration. We further make use of the partial conservation of axial current hypothesis to determine the strong coupling constants $g_{B^{*}B\pi }(0)=60.5\pm 1.1$ and $g_{D^{*}D\pi }(0)=22.1\pm 0.4$. The ratio $R=(g_{B^{*}B\pi }(0)f_{B^{*}}\sqrt{M_D})/(g_{D^{*}D\pi }(0)f_{D^{*}}\sqrt{M_B})=1.105\pm 0.005$ agrees with the heavy quark symmetry prediction of 1.

We use conditions for unitarity cancellations to constrain the couplings of the top and bottom quarks to Kaluza-Klein modes in Higgsless models of electroweak symmetry breaking. An example for the mass spectrum of quark resonances in a theory-space model is given and the implications for the collider phenomenology in the top sector are discussed, comparing to signatures of little Higgs and strong electroweak symmetry breaking models.

We measure the branching fraction and the $CP$-violating asymmetry of $B^0\to K_S^0{\pi }^0$ decays with $227$ million ${\rm Y}(4S)\to B\overline{B}$ events collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC. We obtain a branching fraction $\mathcal{B}(B^0\to K^0{\pi }^0)=(11.4\pm 0.9\pm 0.6)\times {10}^{-6}$ and $CP$-violating asymmetry parameters $C_{K_S^0}{\pi }^0=0.06\pm 0.18\pm 0.03$ and $S_{K_S^0}{\pi }^0={0.35}_{-0.33}^{+0.30}\pm 0.04$, where the first error is statistical and the second systematic.

We use anti–de Sitter/conformal field theory duality to study the thermodynamics of a strongly coupled $\mathcal{N}=2$ supersymmetric large $N_c$ $SU(N_c)$ gauge theory with $N_f=2$ fundamental hypermultiplets. At finite temperature $T$ and isospin chemical potential $\mu$, a potential on the Higgs branch is generated, corresponding to a potential on the moduli space of instantons in the anti–de Sitter description. For $\mu =0$, there is a known first order phase transition around a critical temperature $T_c$. We find that the Higgs vacuum expectation value is a suitable order parameter for this transition; for $T>T_c$, the theory is driven to a nontrivial point on the Higgs branch. For $\mu \ne 0$ and $T=0$, the Higgs potential is unbounded from below, leading to an instability of the field theory due to Bose-Einstein condensation.

We derive the component Lagrangian for a generic $\mathcal{N}=1/2$ supersymmetric chiral model with an arbitrary number of fields in four space-time dimensions. We then investigate a toy model in which the deformation parameter modifies the undeformed potential near the origin of the field space in a way which suggests possible physical applications.

We show that the weight functional for color sources in the classical theory of the color glass condensate (CGC) includes a term which generates odderon excitations. Remarkably, the classical origin of these excitations can be traced to the random walk of partons in the two dimensional space spanned by the SU(3) Casimirs. We compute dipole and baryon odderon operators in the CGC and show that contributions from the classical color sources to these are suppressed in the limit of very large parton densities.

The Misner initial data are a standard example of time-symmetric initial data with two apparent horizons. Compact formulae describing such data are presented in the cases of equal or nonequal masses (i.e. isometric or nonisometric horizons). The interaction energy in the “$\mathrm{\text{Schwarzschild + test-particle}}$” limit of the Misner data is analyzed.

We provide an infinity of spacetimes which contain part of both the Schwarzschild vacuum and de Sitter space. The transition, which occurs below the Schwarzschild event horizon, involves only boundary surfaces (no surface layers). An explicit example is given in which the weak and strong energy conditions are satisfied everywhere (except in the de Sitter section) and the dominant energy condition is violated only in the vicinity of the boundary to the Schwarzschild section. The singularity is avoided by way of a change in topology in accord with a theorem due to Borde.

We investigate the canonical quantization of the electromagnetic field on the Kerr background. We give new expressions for the expectation value of the electromagnetic stress-energy tensor in various quantum states and give a physical interpretation of the separate terms appearing in them. We numerically calculate the luminosity for some of these states. We investigate the form of the renormalized stress-energy tensor close to the horizon when the electromagnetic field is in the past Boulware state.

The brane-world scenario is a new approach to resolve the problem on how to compactify the higher dimensional spacetime to our 4-dimensional world. One of the remarkable features of this scenario is the higher dimensional effects in classical gravitational interactions at short distances. Because of this feature, there are black-string solutions in our 4-dimensional world. In this paper, assuming the simplest model of complex minimally coupled scalar field with the local $U(1)$ symmetry, we show a possibility of black-string formation by merging processes of type I long cosmic strings in our 4-dimensional world. No fine tuning for the parameters in the model might be necessary.

We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, $c$, and $k$ with dimension of velocity. We speculate on different possibilities to relate $k$ with fundamental constants. In particular, expression of $k$ in terms of vacuum energy suggests emergence of (minimum) quantum of mass.

We present a complete quantum mechanical description of a flat Friedmann-Robertson-Walker universe with equation of state $p=\rho$. We find a detailed correspondence with our heuristic picture of such a universe as a dense black hole fluid. Features of the geometry are derived from purely quantum input.

We obtain the equations of motion for cosmic strings in extensions of the $3+1$ Friedmann-Robertson-Walker (FRW) model with extra dimensions. From these we derive a generalization of the velocity-dependent one-scale model for cosmic string network evolution which we apply, first, to a higher-dimensional isotropic $D+1$ FRW model and, second, to a $3+1$ FRW model with static flat extra dimensions. In the former case the string network does not achieve a scaling regime because of the diminishing rate of string intersections ($D>3$), but this can be avoided in the latter case by considering compact, small extra dimensions, for which there is a reduced but still appreciable string intercommuting probability. We note that the velocity components lying in the three expanding dimensions are Hubble damped, whereas those in the static extra dimensions are only very weakly damped. This leads to the pathological possibility, in principle, that string motion in the three infinite dimensions can come to a halt preventing the strings from intersecting, with the result that scaling is not achieved and the strings irreversibly dominate the early universe. We note criteria by which this can be avoided, notably if the spatial structure of the network becomes essentially three-dimensional, as is expected for string networks produced in brane inflation. Applying our model to a brane inflation setting, we find scaling solutions in which the effective 3D string motion does not necessarily stop, but it is slowed down because of the excitations trapped in the extra dimensions. These effects are likely to influence cosmic string network evolution for a long period after formation and we discuss their more general implications.

Closed, singularity-free, inflationary cosmological models have recently been studied in the context of general relativity. Despite their appeal, these so called emergent models suffer from a number of limitations. These include the fact that they rely on an initial Einstein static state to describe the past-eternal phase of the universe. Given the instability of such a state within the context of general relativity, this amounts to a very severe fine tuning. Also in order to be able to study the dynamics of the universe within the context of general relativity, they set the initial conditions for the universe in the classical phase. Here we study the existence and stability of such models in the context of Loop Quantum Cosmology and show that both these limitations can be partially remedied, once semiclassical effects are taken into account. An important consequence of these effects is to give rise to a static solution (not present in GR), which dynamically is a center equilibrium point and located in the more natural semiclassical regime. This allows the construction of emergent models in which the universe oscillates indefinitely about such an initial static state. We construct an explicit emergent model of this type, in which a nonsingular past-eternal oscillating universe enters a phase where the symmetry of the oscillations is broken, leading to an emergent inflationary epoch, while satisfying all observational and semiclassical constraints. We also discuss emergent models in which the universe possesses both early- and late-time accelerating phases.

We use the Hamilton-Jacobi theory to study the nonlinear evolutions of inhomogeneous spacetimes during inflation in generalized gravity. We find the exact solutions to the lowest order Hamilton-Jacobi equation for special scalar potentials and introduce an approximation method for general potentials. The conserved quantity invariant under a change of timelike hypersurfaces proves useful in dealing with gravitational perturbations. In the long-wavelength approximation, we find a conserved quantity related to the new canonical variable that makes the Hamiltonian density vanish, and calculate the non-Gaussianity in generalized gravity. The slow-roll inflation models with a single scalar field in generalized gravity predict too small non-Gaussianity to be detected by future CMB experiments.

We study the rare decays $B_s^0\to D^{\pm }{\pi }^{\mp }$ and ${\overline{B}}_s^0\to D^{\mp }{\pi }^{\pm }$, which can occur only via annihilation type $W$ exchange diagrams in the standard model. The time-dependent decay rates of the four channels can provide four $CP$ parameters, which are experimentally measurable. We show that the Cabibbo-Kobayashi-Maskawa angle ${\varphi }_3=\gamma$ can be determined from these parameters without any theoretical model dependence. These channels can be measured in future LHCb experiments to provide a clean way for $\gamma$ measurement.

We study taste and Euclidean rotational symmetry violation for staggered fermions at nonzero lattice spacing using staggered chiral perturbation theory. We extend the staggered chiral Lagrangian to $\mathcal{O}(a^2{p}^2)$, $\mathcal{O}(a^4)$, and $\mathcal{O}(a^{2}m)$, the orders necessary for a full next-to-leading order calculation of pseudo-Goldstone boson masses and decay constants including analytic terms. We then calculate a number of $SO(4)$ taste-breaking quantities, which involve only a small subset of these next-to-leading order operators. We predict relationships between $SO(4)$ taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. We also find predictions for a few quantities that are not $SO(4)$ breaking. All these results hold also for theories in which the fourth root of the fermionic determinant is taken to reduce the number of quark tastes; testing them will therefore provide evidence for or against the validity of this trick.