We study the discrete causal set geometry of a small causal diamond in a curved spacetime using the average abundance $⟨C_k⟩$ of $k$-element chains or total orders in the underlying causal set $\mathbf{C}$. We begin by obtaining the first-order curvature corrections to the flat spacetime expression for $⟨C_k⟩$ using Riemann normal coordinates. For fixed spacetime dimension this allows us to find a new expression for the discrete scalar curvature of $\mathbf{C}$ as well as the time-time component of its Ricci tensor in terms of the $⟨C_k⟩$. We also find a new dimension estimator for $\mathbf{C}$ which replaces the flat spacetime Myrheim-Meyer estimator in generic curved spacetimes.

We present a covariant derivation of the equations of motion for test bodies for a wide class of gravitational theories with nonminimal coupling, encompassing a general interaction via the complete set of nine parity-even curvature invariants. The equations of motion for spinning test bodies in such theories are explicitly derived by means of Synge’s expansion technique. Our findings generalize previous results in the literature and allow for a direct comparison to the general relativistic equations of motion of pole-dipole test bodies.

Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be rewritten as nonlinear Poincaré algebras with momentum-dependent deformations of commutators between boosts and time translations. In contrast to deformed special relativity, the deformations are derived for generators with an unambiguous physical role, following from the relationship between canonical constraints of gravity with stress-energy components. The original deformation does not appear in momentum space and does not give rise to nonlocality issues or problems with macroscopic objects. Contact with deformed special relativity may help to test loop quantum gravity or restrict its quantization ambiguities.

Newly born neutron stars can present differential rotation, even if later it should be suppressed by viscosity or a sufficiently strong magnetic field. And in this early stage of its life, a neutron star is expected to have a strong emission of gravitational waves, which could be influenced by the differential rotation. We present here a new formalism for modelling differentially rotating neutron stars: working on the slow rotation approximation and assuming a small degree of differential rotation, we show that it is possible to separate variables in the Einstein field equations. The dragging of inertial frames is determined by solving three decoupled ordinary differential equations. After we establish our equilibrium model, we explore the influence of the differential rotation on the $f$- and $r$-modes of oscillation of the neutron star in the Cowling approximation, and we also analyze an effect of the differential rotation on the emission of gravitational radiation from the $f$-modes. We see that the gravitational radiation from the $f$-modes is slightly suppressed by introducing differential rotation to the equilibrium stars.

We examine the nonlinear dynamics of a closed Friedmann-Robertson-Walker universe in the framework of brane world formalism with a timelike extra dimension. In this scenario, the Friedmann equations contain additional terms arising from the bulk-brane interaction, which provide a concrete model for nonsingular bounces in the early phase of the Universe. We construct a nonsingular cosmological scenario sourced with dust, radiation, and a cosmological constant. The structure of the phase space shows a nonsingular orbit with two accelerated phases, separated by a smooth transition corresponding to a decelerated expansion. Given observational parameters we connect such phases to a primordial accelerated phase, a soft transition to Friedmann (where the classical regime is valid), and a graceful exit to a de Sitter accelerated phase.

We study the effect of shear and rotation on results previously obtained dealing with the application of the spherical collapse model (SCM) to generalized Chaplygin gas (gCg)-dominated universes. The system is composed of baryons and gCg and the collapse is studied for different values of the parameter $\alpha$ of the gCg. We show that the joint effect of shear and rotation is that of slowing down the collapse with respect to the simple SCM. This result is of utmost importance for the so-called unified dark matter models, since the described slowdown in the growth of density perturbations can solve one of the main problems of the quoted models, namely the instability described in previous papers [e.g., H. B. Sandvik et al., Phys. Rev. D 69, 123524 (2004)] at the linear perturbation level.

Current theories of the origin of the Universe, including string theory, predict the existence of a multiverse with many bubble universes. These bubble universes may collide, and collisions with ours produce cosmic wakes that enter our Hubble volume, appear as unusually symmetric disks in the cosmic microwave background, and disturb large scale structure. There is preliminary evidence consistent with one or more of these disturbances on our sky. However, other sources can produce similar features in the cosmic microwave background, and so additional signals are needed to verify their extra-universal origin. Here we find, for the first time, the detailed three-dimensional shape, temperature, and polarization signals of the cosmic wake of a bubble collision consistent with current observations. The polarization pattern has distinct features that when correlated with the corresponding temperature pattern are a unique and striking signal of a bubble collision. These features represent a verifiable prediction of the multiverse paradigm and might be detected by current or future experiments. A detection of a bubble collision would confirm the existence of the multiverse, provide compelling evidence for the string theory landscape, and sharpen our picture of the Universe and its origins.

Recently, there have been hints for dark matter (DM) annihilation in the Galactic center to one or more photon lines. In order to achieve the observed photon line flux, DM must have a relatively large effective coupling to photons, typically generated radiatively from large couplings to charged particles. When kinematically accessible, direct annihilation of DM to these charged particles is far too large to accommodate both the DM relic density and constraints from the observed flux of continuum photons from the Galactic center, halo and dwarf galaxies. We discuss three exceptions to these obstacles, generating the observed line signal while providing the correct relic density and evading photon continuum constraints. The exceptions are (i) coannihilation, where the DM density is set by interactions with a heavier state that is not populated today, (ii) forbidden channels, where DM annihilates to heavier states that are kinematically blocked today, but open in the early Universe, and (iii) asymmetric DM, where the relic density is set by a primordial asymmetry. We build simple models to realize these scenarios.

The purely leptonic rare decay $B_s\to {\mu }^{+}{\mu }^{-}$ is very sensitive to supersymmetric contributions which are free from the helicity suppression of its Standard Model diagrams. The recent observation of the decay by the LHCb experiment and the first determination of its branching fraction motivate a review of their impact on the viable parameter space of supersymmetry (SUSY). In this paper we discuss the implications of the present and expected future accuracy on $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ for constrained and unconstrained scenarios of the minimal supersymmetric extension of the Standard Model, in relation to the results from direct SUSY searches and the Higgs data at the LHC. While the constraints from $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ can be very important in specific SUSY regions, we show that the current result, and even foreseen future improvements in its accuracy, will leave a major fraction of the SUSY parameter space, compatible with the results of direct searches, unconstrained. We also highlight the complementarity of the $B_s\to {\mu }^{+}{\mu }^{-}$ decay with direct SUSY searches.

In the context of a conformal supergravity model in the Einstein frame, in which the (next to) minimal supersymmetric standard model can embedded naturally to produce chaotic inflation scenarios, we study properties of gravitino in the cases where it is stable or unstable. In the latter case, we demonstrate that for large dilaton scale factors there is an enhanced magnitude of the gravitino width, when it decays to neutralino dark matter, as compared with the standard supergravity case. In this context, we discuss the associated consequences as far as big bang nucleosynthesis constraints and avoidance of gravitino overproduction are concerned.

Anomaly-mediated supersymmetry breaking (AMSB) is a well-known mechanism for flavor-blind transmission of supersymmetry breaking from the hidden sector to the visible sector. However, the pure AMSB scenario suffers from a serious drawback, namely, the tachyonic slepton problem, and needs to be extended. The so-called (positively) deflected AMSB is a simple extension to solve the problem and also provides us with the usual neutralino lightest superpartner as a good candidate for dark matter in the Universe. Motivated by the recent discovery of the Higgs boson at the Large Hadron Collider (LHC) experiments, we perform the parameter scan in the deflected AMSB scenario by taking into account a variety of phenomenological constraints, such as the dark matter relic density and the observed Higgs boson mass around 125–126 GeV. We identify the allowed parameter region and list benchmark mass spectra. We find that in most of the allowed parameter regions, the dark matter neutralino is Higgsino-like and its elastic scattering cross section with nuclei is within the future reach of the direct dark matter search experiments, while (colored) sparticles are quite heavy and their discovery at the LHC is challenging.

We measure the polarization of $W$ bosons from top-quark ($t$) decays into final states with a charged lepton and jets, $t\overline{t}\to W^{+}b{W}^{-}\overline{b}\to \ell \nu bq{\overline{q}}^{\prime }\overline{b}$, using the full Run II data set collected by the CDF II detector, corresponding to an integrated luminosity of $8.7{\mathrm{fb}}^{-1}$. A model-independent method simultaneously determines the fraction of longitudinal ($f_0$) and right-handed ($f_{+}$) $W$ bosons to yield $f_0=0.726\pm 0.066(\mathrm{stat})\pm 0.067(\mathrm{syst})$ and $f_{+}=-0.045\pm 0.044(\mathrm{stat})\pm 0.058(\mathrm{syst})$ with a correlation coefficient of $-0.69$. Additional results are presented under various standard model assumptions. No significant discrepancies with the standard model are observed.

We report measurements of the branching fractions and direct $CP$ asymmetries (${\mathcal{A}}_{CP}$) for $B\to K\pi$, $\pi \pi$ and $KK$ decays (but not ${\pi }^0{\pi }^0$) based on the final data sample of $772\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We set a 90% confidence-level upper limit for $K^{+}{K}^{-}$ at $2.0\times {10}^{-7}$; all other decays are observed with branching fractions ranging from ${10}^{-6}$ to ${10}^{-5}$. In the $B^0/{\overline{B}}^0\to K^{\pm }{\pi }^{\mp }$ mode, we confirm Belle’s previously reported large ${\mathcal{A}}_{CP}$ with a value of $-0.069\pm 0.014\pm 0.007$ and a significance of $4.4\sigma$. For all other flavor-specific modes, we find ${\mathcal{A}}_{CP}$ values consistent with zero, including ${\mathcal{A}}_{CP}(K^{+}{\pi }^0)=+0.043\pm 0.024\pm 0.007$ with $1.8\sigma$ significance. The difference of $CP$ asymmetry between $B^{\pm }\to K^{\pm }{\pi }^0$ and $B^0/{\overline{B}}^0\to K^{\pm }{\pi }^{\mp }$ is found to be $\Delta {\mathcal{A}}_{K\pi }\equiv {\mathcal{A}}_{CP}(K^{+}{\pi }^0)-{\mathcal{A}}_{CP}(K^{+}{\pi }^{-})=+0.112\pm 0.027\pm 0.007$ with $4.0\sigma$ significance. We also calculate the ratios of partial widths for the $B\to K\pi$ decays. Using our results, we test the validity of the sum rule ${\mathcal{A}}_{CP}(K^{+}{\pi }^{-})+{\mathcal{A}}_{CP}(K^0{\pi }^{+})\frac{\Gamma (K^0{\pi }^{+})}{\Gamma (K^{+}{\pi }^{-})}-{\mathcal{A}}_{CP}(K^{+}{\pi }^0)\frac{2\Gamma (K^{+}{\pi }^0)}{\Gamma (K^{+}{\pi }^{-})}-{\mathcal{A}}_{CP}(K^0{\pi }^0)\frac{2\Gamma (K^0{\pi }^0)}{\Gamma (K^{+}{\pi }^{-})}=0$ and obtain a sum of $-0.270\pm 0.132\pm 0.060$ with $1.9\sigma$ significance.

We study the Casimir interaction between a sphere and a cylinder both subjected to Dirichlet, Neumann, or perfectly conducting boundary conditions. Generalizing the operator approach developed by Wittman [IEEE Trans. Antennas Propag. 36, 1078 (1988)], we compute the scalar and vector translation matrices between a sphere and a cylinder, and thus write down explicitly the exact TGTG formula for the Casimir interaction energy. In the scalar case, the formula shows manifestly that the Casimir interaction force is attractive at all separations. The large separation leading term of the Casimir interaction energy is computed directly from the exact formula. It is of order $\sim \hslash c{R}_1/[L^2\ln (L/R_2)]$, $\sim \hslash c{R}_1^3{R}_2^2/L^6$, and $\sim \hslash c{R}_1^3/[L^4\ln (L/R_2)]$, respectively, for Dirichlet, Neumann, and perfectly conducting boundary conditions, where $R_1$ and $R_2$ are, respectively, the radii of the sphere and the cylinder, and $L$ is the distance between their centers.

In F. Gelis et al. [Phys. Rev. D 78, 054019 (2008).], we have analyzed the leading logarithms of energy that appear in the inclusive spectrum of gluons produced in heavy ion collisions, calculated in the color glass condensate framework. The main result of this paper was that these logarithms are intrinsic properties of the colliding projectiles, and that they can be resummed by letting the distributions of color sources in the nuclei evolve according to the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation. An essential step in the proof of this factorization result is the calculation of the gluon spectrum at next-to-leading order (NLO), and in particular a functional relationship that expresses the NLO correction as the action of a certain operator on the leading order spectrum. In this paper, we show that this type of relation between spectra at leading order and NLO is not specific to the production of gluons, but that it is in fact generic for inclusive spectra in heavy ion collisions. To illustrate this, we compute up to NLO the inclusive spectrum of some hypothetical scalar fields, either color neutral or colored, that couple to gluons.

We present new results on the localization of gauge fields in thick brane models. The four-dimensional observable universe is considered to be a topological defect which is generated by two scalar fields coupled with gravity embedded in a five-dimensional space-time. Like other thick brane models, the Bloch brane setup is not capable of supporting gauge field localization. In order to circumvent this problem we include the dilaton field and, as a result, obtain normalizable solutions. In addition, by writing the equations of motion as Schrödinger-like equations, we have found new kinds of resonances in the massive spectrum which appear also for heavy modes. This is in sharp contrast to what is commonly found in previous analog studies, where only light modes become resonant. At specific energies, the wave solutions exhibit very high amplitudes within the membrane. The influence of the dilaton coupling and of the internal structure on the resonant modes are also discussed.

Here we derive the exact Reissner-Nordström black hole solution on a tensional codimension-2 brane, generalizing earlier Schwarzschild and Kerr results. We begin by briefly reviewing various aspects of codimension-2 branes that will be important for our analysis, including the mechanism of “offloading” of brane tension into the bulk that is unique to these branes, as well as the explicit construction of the codimension-2 Schwarzschild black hole as a warm-up exercise. We then show that the same methods can be used to find the metric describing the spacetime surrounding an electrically charged point source threaded by a codimension-2 brane. The presence of the brane tension leads to an amplification of the apparent strength of gravity, as is well known, and we further find exactly the same enhancement for the apparent strength of the electric field.

We compute the tensorial perturbations to a general spherically symmetric metric in $d$ dimensions with string-theoretical corrections quadratic in the Riemann tensor, from which we derive their respective potential. We use this result to study the stability of corresponding black hole solutions under such perturbations.

We consider a bouncing universe model which explains the flatness of the primordial scalar spectrum via a complex scalar field that rolls down its negative quartic potential and dominates in the universe. We show that in this model there exists a rapid contraction regime of classical evolution. We calculate the power spectrum of tensor modes in this scenario. We find that it is blue and its amplitude is typically small, leading to mild constraints on the parameters of the model.

Turbulence is believed to play important roles in the origin of cosmic magnetism. While it is well known that turbulence can efficiently amplify a uniform or spatially homogeneous seed magnetic field, it is not clear whether or not we can draw a similar conclusion for a localized seed magnetic field. The main uncertainty is the rate of magnetic field diffusion on scales larger than the outer scale of turbulence. To measure the diffusion rate of magnetic field on those large scales, we perform a numerical simulation in which the outer scale of turbulence is much smaller than the size of the system. We numerically compare diffusion of a localized seed magnetic field and a localized passive scalar. We find that diffusion of the magnetic field can be much faster than that of the passive scalar and that turbulence can efficiently amplify the localized seed magnetic field. Based on the simulation result, we construct a model for fast diffusion of magnetic field. Our model suggests that a localized seed magnetic field can fill the whole system in $\sim L_{\mathrm{sys}}/L$ times the large-eddy turnover time and that growth of the magnetic field stops in $\sim \max (15,L_{\mathrm{sys}}/L)$ times the large-eddy turnover time, where $L_{\mathrm{sys}}$ is the size of the system and $L$ is the driving scale. Our finding implies that, regardless of the shape of the seed field, fast magnetization is possible in turbulent systems, such as large-scale structure of the Universe or galaxies.