We point out an inconsistency of a method used in the literature, first advocated by P. Peter and N. Pinto-Neto in [Phys. Rev. D 66, 063509 (2002)], for studying adiabatic scalar perturbations in a regular bouncing universe (in four dimensions). The method under scrutiny consists of splitting the Bardeen potential into two pieces with independent evolutions, in order to avoid a singular behavior at the boundaries of the region where the null energy condition (NEC) is violated. However, we argue that this method violates energy-momentum conservation. We then introduce a novel method which provides two independent solutions for the Bardeen potential around the boundaries, even in the case of adiabatic perturbations. The two solutions are well behaved and not divergent.

We derive some exact results concerning the response of strongly interacting matter to external magnetic fields. Our results come from consideration of triangle anomalies in medium. First, we define an “axial magnetic susceptibility,” then we examine its behavior in two-flavor QCD via response theory. In the chirally restored phase, this quantity is proportional to the fermion chemical potential, while in the phase of broken chiral symmetry it can be related, through triangle anomalies, to an in-medium amplitude for ${\pi }^0\to 2\gamma$. We confirm the latter result by calculation in a linear sigma model, where this amplitude is already known in the literature.

The $S$-matrix form for the polarization tensor of the magnetized vacuum involves an integral over the parallel momentum, $p_z$, and a sum over the Landau levels of the virtual electrons and positrons. When the integrals over $p_z$ are evaluated, they exhibit resonant-type behavior at each of the pair-creation thresholds. Emphasis is initially placed on the regime of soft photons, where simpler integrals are solved. When the sum is taken using the Euler-Maclaurin summation formula and the result is regularized, the known dispersive properties are reproduced for $\omega \ll m$. We evaluate the corrections of order ${\omega }^2$ to these refractive indices and argue that they do not affect the known kinematic selection rules for photon splitting. With a simple modification to the low-frequency results, refractive indices are evaluated at frequencies up to just above the first pair-creation threshold, for supercritical magnetic fields.

We consider how Lorentz-violating interactions in the Faddeev-Popov ghost sector will affect scalar QED. The behavior depends sensitively on whether the gauge symmetry is spontaneously broken. If the symmetry is not broken, Lorentz violations in the ghost sector are unphysical, but if there is spontaneous breaking, radiative corrections will induce Lorentz-violating and gauge-dependent terms in other sectors of the theory.

At sufficiently high densities, cold dense three-flavor quark matter is in the color-flavor locked (CFL) phase, in which all nine quarks pair in a particularly symmetric fashion. Once the heaviness of the strange quark (mass $m_s$) and the requirements of electric and color neutrality are taken into account, the CFL pattern of color superconductivity requires the pairing of quarks that would, in the absence of pairing, have Fermi momenta that differ by of order $m_s^2/\mu$, with $\mu$ the quark number chemical potential. This means that at sufficiently small $\mu$, the “stress” on the pairing is large enough that the system can lower its energy by breaking pairs, resulting in some unconventional color superconductor which includes gapless excitations, spatial inhomogeneity, counter-propagating currents, or all three. In this paper we ask whether there is some less symmetric but still conventional pattern of pairing that can evade the stress. In other words, is there a pattern of pairing in which, once electric and color neutrality are imposed by suitable chemical potentials, pairing only occurs among those quarks whose Fermi momenta would be equal in the absence of pairing? We use graph-theoretical methods to classify 511 patterns of conventional color-superconducting pairing, and show that none of them meet this requirement. All feel a stress, and all can be expected to become unstable to gapless modes at a density comparable to that at which the CFL phase becomes unstable.

We compute the dimensionless relativistic periastron advance parameter $k$, which is measurable from the timing of relativistic binary pulsars. We present a new (general) method and employ for the computation the recently derived Keplerian-type parametric solution to the post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The parametric solution and hence the parameter $k$ are applicable for the cases of simple precession, namely, case (i), the binary consists of equal-mass compact objects, having two arbitrary spins, and case (ii), the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. Our expression, for the cases considered, is in agreement with a more general formula for the 2PN accurate $k$, relevant for the relativistic double pulsar PSR J0737–3039, derived by Damour and Schäfer many years ago, using a different procedure.

The low energy regime of 5D braneworld models with a bulk scalar field is studied. The setup is rather general and includes the Randall-Sundrum and dilatonic braneworlds models as particular cases. We discuss the cosmological evolution of the system and conclude that, in a two brane system, the negative tension brane is generally expected to evolve towards a null warp-factor state. This implies, for late time cosmology, that both branes end up interacting weakly. We also analyze the observational constraints imposed by solar-system and binary-pulsar tests on the braneworld configuration. This is done by considering the small deviations produced by the branes on the 4D gravitational interaction between bodies in the same brane. Using these constraints we show that the geometry around the braneworld is strongly warped, and that both branes must be far apart.

We investigate the thermodynamics of static black objects such as black holes, black strings and their generalizations to $D$ dimensions (“black branes”) in a gravitational theory containing the four-dimensional Gauss-Bonnet term in the action, with $D-4$ dimensions compactified torus. The entropies of black holes and black branes are compared to obtain information on the stability of these objects and to find their phase diagrams. We demonstrate the existence of a critical mass, which depends on the scale of the compactified dimensions, below which the black hole entropy dominates over the entropy of the black membrane.

Cosmological models of Bianchi types V and I containing a perfect fluid with a linear equation of state plus cosmological constant are investigated. In general, these spacetimes are tilted and describe fluids with expansion, shear, and vorticity. We use a tetrad approach where our variables are the Riemann tensor, the Ricci rotation coefficients, and a subset of the tetrad vector components. This set, called $S$, describes a spacetime when its elements are constrained by certain integrability conditions and due to a theorem by Cartan $S$ gives a complete local description of the spacetime. With the help of the Lie algebra, the full line element is constructed up to quadratures in terms of the elements in $S$. The system obtained by imposing the integrability conditions and Einstein’s equations on the elements in $S$ can be reduced to an integrable system of five coupled first order ordinary differential equations. In general, exact solutions to this system are hard to find, but the linearized equations around the open Friedmann models are easily integrated. The full system is also studied numerically and the perturbative solutions agree well with the numerical ones in the appropriate domains. We also give some examples of numerical solutions in the nonperturbative regime.

One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem—the existence of well-behaved regularization of the constraints—is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the $SU(2)$ unitary representation used in the diffeomorphism covariant “point-splitting” regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer $m$ and, here, it is referred to as the $m$ ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study $2+1$ gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in $2+1$ loop quantum gravity. We then analyze the effects of the ambiguity in $3+1$ gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in $3+1$ dimensions—due to the difficulties associated to the definition of the physical inner product—it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is $SO(3)$ we find physical solutions associated to spin-two local excitations.

We construct Gödel-type black hole and particle solutions to Einstein-Maxwell theory in $2+1$ dimensions with a negative cosmological constant and a Chern-Simons term. On-shell, the electromagnetic stress-energy tensor effectively replaces the cosmological constant by minus the square of the topological mass and produces the stress-energy of a pressure-free perfect fluid. We show how a particular solution is related to the original Gödel universe and analyze the solutions from the point of view of identifications. Finally, we compute the conserved charges and work out the thermodynamics.

We study the generation and evolution of gravitational waves (tensor perturbations) in the context of Randall-Sundrum braneworld cosmology. We assume that the initial and final stages of the background cosmological model are given by de Sitter and Minkowski phases, respectively, and they are connected smoothly by a radiation-dominated phase. This setup allows us to discuss the quantum-mechanical generation of the perturbations and to see the final amplitude of the well-defined zero mode. Using the Wronskian formulation, we numerically compute the power spectrum of gravitational waves, and find that the effect of initial vacuum fluctuations in the Kaluza-Klein modes is subdominant, contributing not more than 10% of the total power spectrum. Thus it is confirmed that the damping due to the Kaluza-Klein mode generation and the enhancement due to the modification of the background Friedmann equation are the two dominant effects, but they cancel each other, leading to the same spectral tilt as the standard four-dimensional result. Kaluza-Klein gravitons that escape from the brane contribute to the energy density of the dark radiation at late times. We show that a tiny amount of the dark radiation is generated due to this process.

In this work we study to which extent the knowledge of spatial topology may place constraints on the parameters of the generalized Chaplygin gas (GCG) model for unification of dark energy and dark matter. By using both the Poincaré dodecahedral and binary octahedral spaces as the observable spatial topologies, we examine the current type Ia supernovae (SNe Ia) constraints on the GCG model parameters. We show that the knowledge of spatial topology does provide additional constraints on the $A_s$ parameter of the GCG model but does not lift the degeneracy of the $\alpha$ parameter.

Several analyses of the microwave sky maps from the Wilkinson Microwave Anisotropy Probe (WMAP) have drawn attention to alignments amongst the low-order multipoles. Amongst the various possible explanations, an effect of cosmic topology has been invoked by several authors. We focus on an alignment of the first four multipoles ($\ell =2$ to 5) found by Land and Magueijo (2005), and investigate the distribution of their alignment statistic for a set of simulated cosmic microwave background maps for cosmologies with slablike topology. We find that this topology does offer a modest increase in the probability of the observed value, but that even for the smallest topology considered the probability of the observed value remains below 1%.

Experiment 865 at the Brookhaven AGS has observed the decay $K^{+}\to e^{+}{\nu }_e{\mu }^{+}{\mu }^{-}$. The branching ratio extracted is $(1.72\pm 0.37(\mathrm{stat})\pm 0.17(\mathrm{syst})\pm 0.19(\mathrm{model}))\times {10}^{-8}$ where the third term in the error results from the use of a model to extrapolate into a kinematic region dominated by background.

We discuss possible sgoldstino interpretation of the observation, reported by HyperCP collaboration, of three ${\Sigma }^{+}\to p{\mu }^{+}{\mu }^{-}$ decay events with dimuon invariant mass $214.3$ MeV within detector resolution. We find that this interpretation is consistent in models with (i) parity conservation in sgoldstino interactions, (ii) pseudoscalar sgoldstino $P$ of mass $214$ MeV and heavier scalar sgoldstino, and (iii) low supersymmetry breaking scale, $\sqrt{F}=2.5$-$60$ TeV. In these models, sgoldstino can be observed in decays $K^{+}\to {\pi }^{+}{\pi }^{0}P$, $K_L\to \pi \pi P$ and $K_S\to \pi \pi P$ at the branching ratios of at least of order ${10}^{-12}$, ${10}^{-8}$ and ${10}^{-11}$, respectively. The model can be probed also at $e^{+}{e}^{-}$ colliders in the channels $e^{+}{e}^{-}\to \gamma P$ and $e^{+}{e}^{-}\to e^{+}{e}^{-}P$, where the cross section is likely to be in the range 1 pb–5 ab.

The existence in the physical QCD vacuum of nonzero gluon condensates, such as $⟨g^2{F}^2⟩$, requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit “topological charge” $q$ characterizing the fields approximating the gluon configurations which should dominate the QCD partition function. If $q$ is an irrational number then the critical values of the $\theta$ parameter for which $CP$ is spontaneously broken are dense in $\mathbb{R}$, which provides for a mechanism of resolving the strong $CP$ problem simultaneously with a correct implementation of $U_{\mathrm{A}}(1)$ symmetry. We present an explicit realization of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.

We study the final state interaction effects in $B\to KK$ decays. We find that the $t$ channel one-particle-exchange diagrams cannot enhance the branching ratios of ${\overline{B}}^0\to K^0{\overline{K}}^0$ and $B^{-}\to K^0{K}^{-}$ very sizably. For the pure annihilation process ${\overline{B}}^0\to K^{+}{K}^{-}$, the obtained branching ratio by the final state interaction is at $\mathcal{O}({10}^{-8})$.

With the identification of $(D_{sJ}(2317),D_{sJ}(2460))$ as the $(0^{+},1^{+})$ doublet in the heavy quark effective field theory, we derive the light-cone QCD sum rule for the coupling of an eta meson with $D_{sJ}(2317)D_s$ and $D_{sJ}(2460)D_s^{*}$. Through $\eta -{\pi }^0$ mixing we calculate their pionic decay widths, which are consistent with the experimental values (or upper limits). Combining the radiative decay widths derived by Colangelo, Fazio, and Ozpineci in the same framework, we conclude that the decay patterns of $D_{sJ}(2317,2460)$ strongly support their interpretation as ordinary $c\overline{s}$ mesons.

We develop an extension of chiral perturbation theory to the $\Delta (1232)$-resonance energy region and apply it to investigate the pion electroproduction off the nucleon ($e^{-}N\to e^{-}N\pi$). We present a complete calculation of this process, in the $\Delta$-resonance region, up to next-to-leading order in the $\delta$ expansion. At this order, the only free parameters are the three low-energy constants corresponding to the magnetic ($M1$), electric ($E2$), and Coulomb ($C2$) $\gamma N\to \Delta$ transition strength. After fitting these parameters to a few well-known data, our calculation provides a prediction for observables and multipole amplitudes of pion electroproduction. These results compare favorably with the phenomenological multipole solutions and recent experimental results from MIT-Bates and MAMI. Our prediction for the pion-mass dependence of the $\gamma N\Delta$ form factors offers an explanation for the discrepancy between the recent lattice-QCD results and the experimental value for the “$C2/M1$ ratio” at low $Q^2$.