Conditions for low-redshift positive apparent acceleration in smooth inhomogeneous models

It is known that a smooth LTB model cannot have a positive apparent central acceleration. Using a local Taylor expansion method we study the low-redshift conditions to obtain an apparent negative deceleration parameter $q^{app}(z)$ derived from the luminosity distance $D_L(z)$ for a central observer in a LTB space, confirming that central smoothness implies a positive central deceleration. Since observational data is only available at redshift greater than zero we find the critical values of the parameters defining a centrally smooth LTB model which give a positive apparent acceleration at $z>0$ , providing a graphical representation of the conditions in the $q_0^{app},q_1^{app}$ plane, which are respectively the zero and first order terms of the central Taylor expansion of $q^{app}(z)$ . We finally derive a coordinate independent expression for the apparent deceleration parameter based on the expansion of the relevant functions in red-shift rather than in the radial coordinate. We calculate $q^{app}(z)$ with two different methods to solve the null geodesic equations, one based on a local central expansion of the solution in terms of cosmic time and the other one using the exact analytical solution in terms of generalized conformal time.     

Gravitational collapse with tachyon field and barotropic fluid

A particular class of space-time, with a tachyon field, $\phi $ , and a barotropic fluid constituting the matter content, is considered herein as a model for gravitational collapse. For simplicity, the tachyon potential is assumed to be of inverse square form i.e., $V(\phi )\sim \phi ^{-2}$ . Our purpose, by making use of the specific kinematical features of the tachyon, which are rather different from a standard scalar field, is to establish the several types of asymptotic behavior that our matter content induces. Employing a dynamical system analysis, complemented by a thorough numerical study, we find classical solutions corresponding to a naked singularity or a black hole formation. In particular, there is a subset where the fluid and tachyon participate in an interesting tracking behaviour, depending sensitively on the initial conditions for the energy densities of the tachyon field and barotropic fluid. Two other classes of solutions are present, corresponding respectively, to either a tachyon or a barotropic fluid regime. Which of these emerges as dominant, will depend on the choice of the barotropic parameter, $\gamma $ . Furthermore, these collapsing scenarios both have as final state the formation of a black hole.     

Toward a Mathematical Holographic Principle

In work started in [17] and continued in this paper our objective is to study selectors of multivalued functions which have interesting dynamical properties, such as possessing absolutely continuous invariant measures. We specify the graph of a multivalued function by means of lower and upper boundary maps \(\tau _{1}\) and \(\tau _{2}.\) On these boundary maps we define a position dependent random map \(R_{p}=\{\tau _{1},\tau _{2};p,1-p\},\) which, at each time step, moves the point \(x\) to \(\tau _{1}(x)\) with probability \(p(x)\) and to \(\tau _{2}(x)\) with probability \(1-p(x)\) . Under general conditions, for each choice of \(p\) , \(R_{p}\) possesses an absolutely continuous invariant measure with invariant density \(f_{p}.\) Let \(\varvec{\tau }\) be a selector which has invariant density function \(f.\) One of our objectives is to study conditions under which \(p(x)\) exists such that \(R_{p}\) has \(f\) as its invariant density function. When this is the case, the long term statistical dynamical behavior of a selector can be represented by the long term statistical behavior of a random map on the boundaries of \(G.\) We refer to such a result as a mathematical holographic principle. We present examples and study the relationship between the invariant densities attainable by classes of selectors and the random maps based on the boundaries and show that, under certain conditions, the extreme points of the invariant densities for selectors are achieved by bang-bang random maps, that is, random maps for which \(p(x)\in \{0,1\}.\)      

Suppression of Decoherence by Periodic Forcing

We consider a finite-dimensional quantum system coupled to a thermal reservoir and subject to a time-periodic, energy conserving forcing. We show that, if a certain dynamical decoupling condition is fulfilled, then the periodic forcing counteracts the decoherence induced by the reservoir: for small system–reservoir coupling $\lambda $ and small forcing period $T$ , the system dynamics is approximated by an energy conserving and non-dissipative dynamics, which preserves coherences. For times up to order $(\lambda T)^{-1}$ , the difference between the true and approximated dynamics is of size $\lambda +T$ . Our approach is rigorous and combines Floquet and spectral deformation theory. We illustrate our results on the spin-fermion model and recover previously known, heuristically obtained results.     

Global observables at PHENIX

We present PHENIX recent results on charged particle and transverse energy densities measured at mid-rapidity in Au?Au collisions at $\sqrt {s_{NN} } = 130$ GeV and 200 GeV over a broad range of centralities. The mean transverse energy per charged particle is derived. The first PHENIX measurements at $\sqrt {s_{NN} } = 19.6$ GeV are also presented. A comparison with calculations from various theoretical models is performed.     

Double inclusive cross sections for gluon production in collision of two projectiles on two targets in the BFKL approach

We compute the normalization of the form factor entering the $B_{s}\rightarrow D_{s}\ell \nu $ decay amplitude by using numerical simulations of QCD on the lattice. From our study with $N_\mathrm{f}=2$ dynamical light quarks, and by employing the maximally twisted Wilson quark action, we obtain in the continuum limit ${\mathcal {G}}(1)= 1.052(46)$ . We also compute the scalar and tensor form factors in the region near zero recoil and find $f_0(q_0^2)/f_+(q_0^2)=0.77(2)$ , $f_T(q_0^2,m_b)/f_+(q_0^2)=1.08(7)$ , for $q_0^2=11.5\ \mathrm{GeV}^2$ . The latter results are useful for searching the effects of physics beyond the Standard Model in $B_{s}\rightarrow D_{s}\ell \nu $ decays. Our results for the similar form factors relevant to the non-strange case indicate that the method employed here can be used to achieve the precision determination of the $B\rightarrow D\ell \nu $ decay amplitude as well.     

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, ${\mathcal{E}}$ , on a subspace, ${\mathcal{T}}$ , of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from pure gauge perturbations and perturbations towards other stationary black holes— ${\mathcal{E}}$ is nondegenerate on ${\mathcal{T}}$ and that, for axisymmetric perturbations, ${\mathcal{E}}$ has positive flux properties at both infinity and the horizon. We further show that ${\mathcal{E}}$ is related to the second order variations of mass, angular momentum, and horizon area by ${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$ , thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with ${\mathcal{E} < 0}$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of ${\mathcal{E}}$ on ${\mathcal{T}}$ is equivalent to the satisfaction of a “ local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action.     

Reissner–Nordström thin-shell wormholes with generalized cosmic Chaplygin gas

Following Visser’s approach (Visser in Phys. Rev. D 39:3182, 1989; Nucl. Phys. B 328:203, 1989; Lorentzian wormholes. AIP Press, New York, 1996) of cut and paste, we construct Reissner–Nordström thin-shell wormholes by taking the generalized cosmic Chaplygin gas for the exotic matter located at the wormhole throat. The Darmois–Israel conditions are used to determine the dynamical quantities of the system. The viability of the thin-shell wormholes is explored with respect to radial perturbations preserving the spherical symmetry. We find stable as well as unstable Reissner–Nordström thin-shell wormhole solutions depending upon the model parameters. Finally, we compare our results with both generalized and modified Chaplygin gases.     

Semiclassical strings in supergravity PFT

In this paper, we introduce the bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function \(f(R,T)\) , where \(R\) and \(T\) denote the curvature scalar and the trace of the energy–momentum tensor, respectively, within the framework of a flat Friedmann–Robertson–Walker model. As an equation of state for a prefect fluid, we take \(p=(\gamma -1)\rho \) , where \(0 \le \gamma \le 2\) and a viscous term as a bulk viscosity due to the isotropic model, of the form \(\zeta =\zeta _{0}+\zeta _{1}H\) , where \(\zeta _{0}\) and \(\zeta _{1}\) are constants, and \(H\) is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non-viscous and viscous fluids, respectively, by assuming a simplest particular model of the form of \(f(R,T) = R+2f(T)\) , where \(f(T)=\alpha T\) ( \(\alpha \) is a constant). A big-rip singularity is also observed for \(\gamma <0\) at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of \(\alpha \) to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits a transition from a decelerated phase to an accelerated phase under certain constraints of \(\zeta _0\) and \(\zeta _1\) . We compare the viscous models with the non-viscous one through the graph plotted between the scale factor and cosmic time and find that the bulk viscosity plays a major role in the expansion of the universe. A similar graph is plotted for the deceleration parameter with non-viscous and viscous fluids and we find a transition from decelerated to accelerated phase with some form of bulk viscosity.     

A special exact spherically symmetric solution in f(T) gravity theories

A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate $r$ r , is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is obtained. The scalar torsion related to this special solution vanishes. To understand the physical meaning of the constant of integration we calculate the energy associated with this solution and show how it is related to the gravitational mass of the system.     

Branes as solutions of gauge theories in gravitational field

In this paper we study the behavior of the jet quenching parameter in a background metric with hyperscaling violation at finite temperature. The background metric is covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent \(z\) and hyperscaling exponent \(\theta \) . We have evaluated the jet quenching parameter for a certain range of these parameters which are consistent with the Gubser bound conditions in terms of \(T\) , \(z\) , and \(\theta \) . The results are compared with those of experimental data as well as conformal and the non-conformal cases. Finally, we add a constant electric field to the background and find its effect on the jet quenching parameter.     

Proton-antiproton annihilation into a \Lambda_{c}^{+} \bar{{\Lambda}}_{c}^{-} pair

The process p $ \bar{{p}}$ $ \rightarrow$ $ \Lambda_{c}^{+}$ $ \bar{{\Lambda}}_{c}^{-}$ is investigated within the handbag approach. It is shown to lowest order of perturbative QCD that, under the assumption of restricted parton virtualities and transverse momenta, the dominant dynamical mechanism, characterized by the partonic subprocess u $ \bar{{u}}$ $ \rightarrow$ c $ \bar{{c}}$ , factorizes in the sense that only the subprocess contains highly virtual partons, namely a gluon, while the hadronic matrix elements embody only soft scales and can be parameterized in terms of helicity flip and non-flip generalized parton distributions. Modelling the latter functions by overlaps of light-cone wave functions for the involved baryons we are able to predict cross-sections and spin correlation parameters for the process of interest.     

F(T) gravity and k-essence

Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible candidate of dark energy. We perform a thorough reconstruction analysis on the so-called $F(T)$ models, where $F(T)$ is some general function of the torsion term. We derive conditions for the equivalence between of $F(T)$ models with purely kinetic k-essence. We present a new class models of $F(T)$ gravity and k-essence.     

Wahlquist’s metric versus an approximate solution with the same equation of state

We compare an approximation of the singularity-free Wahlquist exact solution with a stationary and axisymmetric metric for a rigidly rotating perfect fluid with the equation of state $\mu +3p=\mu _0$ , a sub-case of a global approximate metric obtained recently by some of us. We see that to have a fluid with vanishing twist vector everywhere in Wahlquist’s metric the only option is to let its parameter $r_0\rightarrow 0$ and using this in the comparison allows us in particular to determine the approximate relation between the angular velocity of the fluid in a set of harmonic coordinates and $r_0$ . Through some coordinate changes we manage to make every component of both approximate metrics equal. In this situation, the free constants of our metric take values that happen to be those needed for it to be of Petrov type D, the last condition that this fluid must verify to give rise to the Wahlquist solution.     

Energy conditions in f(R,G) gravity

Modified gravity is one of the most favorable candidates for explaining the current accelerating expansion of the Universe. In this regard, we study the viability of an alternative gravitational theory, namely $f(R,G)$ , by imposing energy conditions. We consider two forms of $f(R,G)$ , commonly discussed in the literature, which account for the stability of cosmological solutions. We construct the inequalities obtained by energy conditions and specifically apply the weak energy condition using the recent estimated values of the Hubble, deceleration, jerk and snap parameters to probe the viability of the above-mentioned forms of $f(R, G)$ .     

Analyticity of \eta \pi isospin-violating form factors and the \tau \rightarrow \eta \pi \nu second-class decay

We consider the evaluation of the \(\eta \pi \) isospin-violating vector and scalar form factors relying on a systematic application of analyticity and unitarity, combined with chiral expansion results. It is argued that the usual analyticity properties do hold (i.e. no anomalous thresholds are present) in spite of the instability of the \(\eta \) meson in QCD. Unitarity relates the vector form factor to the \(\eta \pi \rightarrow \pi \pi \) amplitude: we exploit progress in formulating and solving the Khuri–Treiman equations for \(\eta \rightarrow 3\pi \) and in experimental measurements of the Dalitz plot parameters to evaluate the shape of the \(\rho \) -meson peak. Observing this peak in the energy distribution of the \(\tau \rightarrow \eta \pi \nu \) decay would be a background-free signature of a second-class amplitude. The scalar form factor is also estimated from a phase dispersive representation using a plausible model for the \(\eta \pi \) elastic scattering \(S\) -wave phase shift and a sum rule constraint in the inelastic region. We indicate how a possibly exotic nature of the \(a_0(980)\) scalar meson manifests itself in a dispersive approach. A remark is finally made on a second-class amplitude in the \(\tau \rightarrow \pi \pi \nu \) decay.     

An interacting dark energy model in a non-flat universe

In this paper, an interacting dark energy model in a non-flat universe is studied, with taking interaction form $C=\alpha H\rho _{de}$ C = α H ρ d e . And in this study a property for the mysterious dark energy is aforehand assumed, i.e. its equation of state $w_{\Lambda }=-1$ w Λ = - 1 . After several derivations, a power-law form of dark energy density is obtained $\rho _{\Lambda } \propto a^{-\alpha }$ ρ Λ ∝ a - α , here $a$ a is the cosmic scale factor, $\alpha $ α is a constant parameter introducing to describe the interaction strength and the evolution of dark energy. By comparing with the current cosmic observations, the combined constraints on the parameter $\alpha $ α is investigated in a non-flat universe. For the used data they include: the Union2 data of type Ia supernova, the Hubble data at different redshifts including several new published datapoints, the baryon acoustic oscillation data, the cosmic microwave background data, and the observational data from cluster X-ray gas mass fraction. The constraint results on model parameters are $\Omega _{K}=0.0024\,(\pm 0.0053)^{+0.0052+0.0105}_{-0.0052-0.0103}, \alpha =-0.030\,(\pm 0.042)^{+0.041+0.079}_{-0.042-0.085}$ Ω K = 0.0024 ( ± 0.0053 ) - 0.0052 - 0.0103 + 0.0052 + 0.0105 , α = - 0.030 ( ± 0.042 ) - 0.042 - 0.085 + 0.041 + 0.079 and $\Omega _{0m}=0.282\,(\pm 0.011)^{+0.011+0.023}_{-0.011-0.022}$ Ω 0 m = 0.282 ( ± 0.011 ) - 0.011 - 0.022 + 0.011 + 0.023 . According to the constraint results, it is shown that small constraint values of $\alpha $ α indicate that the strength of interaction is weak, and at $1\sigma $ 1 σ confidence level the non-interacting cosmological constant model can not be excluded.     

Poincaré-Dulac Normal Form Reduction for Unconditional Well-Posedness of the Periodic Cubic NLS

We implement an infinite iteration scheme of Poincaré-Dulac normal form reductions to establish an energy estimate on the one-dimensional cubic nonlinear Schrödinger equation (NLS) in ${C_tL^2(\mathbb{T})}$ C t L 2 ( T ) , without using any auxiliary function space. This allows us to construct weak solutions of NLS in ${C_tL^2(\mathbb{T})}$ C t L 2 ( T ) with initial data in ${L^2(\mathbb{T})}$ L 2 ( T ) as limits of classical solutions. As a consequence of our construction, we also prove unconditional well-posedness of NLS in ${H^s(\mathbb{T})}$ H s ( T ) for ${s \geq \frac{1}{6}}$ s ≥ 1 6 .