Perturbations of a perfect barotropic and irrotational Newtonian self-gravitating fluid are studied using a generalization of the so-called “effective geometry” formalism. The case of polytropic spherical stars, as described by the Lane-Emden equation, is studied in detail in the known cases of existing explicit solutions. The present formulation gives a natural scenario in which the acoustic analogy has relevance for both stellar and galactic dynamics.

We examine the separability properties of the equation of motion for a stationary string near a rotating charged black hole with two independent angular momenta in five-dimensional minimal gauged supergravity. It is known that the separability problem for the stationary string in a general stationary spacetime is reduced to that for the usual Hamilton-Jacobi equation for geodesics of its quotient space with one dimension fewer. Using this fact, we show that the “effective metric” of the quotient space does not allow the complete separability for the Hamilton-Jacobi equation, albeit such a separability occurs in the original spacetime of the black hole. We also show that only for two special cases of interest the Hamilton-Jacobi equation admits the complete separation of variables and therefore the integrability for the stationary string motion in the original background, namely, when the black hole has zero electric charge or it has an arbitrary electric charge but two equal angular momenta. We give the explicit expressions for the Killing tensors corresponding to these cases. However, for the general black hole spacetime the effective metric of the quotient space admits a conformal Killing tensor. We construct the explicit expression for this tensor.

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.

A component of dark energy has been recently proposed to explain the current acceleration of the Universe. Unless some unknown symmetry in Nature prevents or suppresses it, such a field may interact with the pressureless component of dark matter, giving rise to the so-called models of coupled quintessence. In this paper we propose a new cosmological scenario where radiation and baryons are conserved, while the dark energy component is decaying into cold dark matter. The dilution of cold dark matter particles, attenuated with respect to the usual $a^{-3}$ scaling due to the interacting process, is characterized by a positive parameter $ϵ$, whereas the dark energy satisfies the equation of state $p_x=\omega {\rho }_x$ ($\omega <0$). We carry out a joint statistical analysis involving recent observations from type Ia supernovae, baryon acoustic oscillation peak, and cosmic microwave background shift parameter to check the observational viability of the coupled quintessence scenario here proposed.

Extending the approach developed by Araújo and Stoeger [M. E. Araújo and W. R. Stoeger, Phys. Rev. D 60, 104020 (1999)] and improved in Araújo et al. [M. E. Araújo, S. R. M. M. Roveda, and W. R. Stoeger, Astrophys. J. 560, 7 (2001)], we have shown how to construct dust-filled $\Lambda \ne 0$ Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological models from FLRW cosmological data on our past light cone. Apart from being of interest in its own right—demonstrating how such data fully determines the models—it is also illustrated in the flat case how the more general spherically symmetric Einstein field equations can be integrated in observational coordinates with data fit to FLRW forms arrayed on our past light cone, thus showing how such data determines an FLRW universe—which is not a priori obvious. It is also shown how to integrate these exact sypherically symmetric equations, in cases where the data are not FLRW, and the space-time is not known to be flat. It is essential for both flat and nonflat cases to have data giving the maximum of the observer area (angular-diameter) distance, and the redshift $z_{\max }$ at which that occurs. This enables the determination of the vacuum-energy density ${\mu }_{\Lambda }$, which would otherwise remain undetermined.

The observational effect of all minimally coupled scalar field models of dark energy can be determined by the behavior of the following two parameters: (1) equation of state parameter $w$, which relates dark energy pressure to its energy density, and (2) effective speed of sound $c_e^2$, which relates dark energy pressure fluctuation to its density fluctuation. In this paper we show that these two parameters do not uniquely determine the form of a scalar field dark energy Lagrangian even after taking into account the perturbation in the scalar field. We present this result by showing that two different forms of scalar field Lagrangian can lead to the same values for these paired parameters. It is well known that from the background evolution the Lagrangian of the scalar field dark energy cannot be uniquely determined. The two models of dark energy presented in this paper are indistinguishable from the evolution of background as well as from the evolution of perturbations from a Friedmann-Robertson-Walker metric.

Using plaquette and Symanzik improved gauge action and stout link clover fermions we determine the improvement coefficient $c_{SW}$ in one-loop lattice perturbation theory from the off-shell quark-quark-gluon three-point function. In addition, we compute the coefficients needed for the most general form of quark field improvement and present the one-loop result for the critical hopping parameter ${\kappa }_c$. We discuss mean field improvement for $c_{SW}$ and ${\kappa }_c$ and the choice of the mean field coupling for the actions we have considered.

In nonrelativistic QCD, we study $e^{+}{e}^{-}\to J/\psi (\psi (2S))+{\chi }_{c0}$ at $B$ factories, where the P-wave state ${\chi }_{c0}$ is associated with a S-wave state $J/\psi$ or $\psi (2S)$. In contrast to the failure of factorization in most cases involving P-wave states, e.g. in $B$ decays, we find that factorization holds in this process at next-to-leading order (NLO) in ${\alpha }_s$ and leading order in $v$, where the associated S-wave state plays a crucial rule in canceling the infrared divergences. We also give some general analyses for factorization in various double charmonium production. The NLO corrections in $e^{+}{e}^{-}\to J/\psi (\psi (2S))+{\chi }_{c0}$ at $\sqrt{s}=10.6\mathrm{GeV}$ are found to substantially enhance the cross sections by a factor of about 2.8; hence crucially reducing the large discrepancy between theory and experiment. With $m_c=1.5\mathrm{GeV}$ and $\mu =2m_c$, the NLO cross sections are estimated to be 17.9(11.3) fb for $e^{+}{e}^{-}\to J/\psi (\psi (2S))+{\chi }_{c0}$, which reach the lower bounds of the experiment.

We investigate the axial-vector transition constants of the baryon antidecuplet to the octet and decuplet within the framework of the self-consistent SU(3) chiral quark-soliton model. Taking into account rotational $1/N_c$ and linear $m_s$ corrections and using the symmetry-conserving quantization, we calculate the axial-vector transition constants. It is found that the leading-order contributions are generally almost canceled by the rotational $1/N_c$ corrections. Thus, the $m_s$ corrections turn out to be essential contributions to the axial-vector constants. The decay width of the ${\Theta }^{+}\to NK$ transition is determined to be $\Gamma (\Theta \to NK)=0.71\mathrm{MeV}$, based on the result of the axial-vector transition constant $g_A^{*}(\Theta \to NK)=0.05$. In addition, other strong decays of the baryon antidecuplet are investigated. The forbidden decays from the baryon antidecuplet to the decuplet are also studied.

Using $214{\mathrm{fb}}^{-1}$ of data recorded by the BABAR detector at the PEPII electron-positron collider, we study the decay $D_s^{+}\to K^{+}{K}^{-}{e}^{+}{\nu }_e$. Except for a small S-wave contribution, the events with $K^{+}{K}^{-}$ masses in the range $1.01–1.03\mathrm{GeV}/c^2$ correspond to $\varphi$ mesons. For $D_s^{+}\to \varphi e^{+}{\nu }_e$ decays, we measure the relative normalization of the Lorentz invariant form factors at $q^2=0$, $r_V=V(0)/A_1(0)=1.849\pm 0.060\pm 0.095$, $r_2=A_2(0)/A_1(0)=0.763\pm 0.071\pm 0.065$ and the pole mass of the axial-vector form factors $m_A=({2.28}_{-0.18}^{+0.23}\pm 0.18)\mathrm{GeV}/c^2$. Within the same $K^{+}{K}^{-}$ mass range, we also measure the relative branching fraction $\mathcal{B}(D_s^{+}\to K^{+}{K}^{-}{e}^{+}{\nu }_e)/\mathcal{B}(D_s^{+}\to K^{+}{K}^{-}{\pi }^{+})=0.558\pm 0.007\pm 0.016$, from which we obtain the total branching fraction $\mathcal{B}(D_s^{+}\to \varphi e^{+}{\nu }_e)=(2.61\pm 0.03\pm 0.08\pm 0.15)\times {10}^{-2}$. By comparing this value with the predicted decay rate, we extract $A_1(0)=0.607\pm 0.011\pm 0.019\pm 0.018$. The stated uncertainties are statistical, systematic, and from external inputs.

We systematically classify all possible Bogomol’nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\le 8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a general method allowing to obtain the BPS equations in any dimension. In addition, we find all BPS equations in the Minkowski space of dimension $d\le 6$ and apply the obtained results to the supersymmetric Yang-Mills theories. In conclusion, we discuss the possibility of using the classification to construct soliton solutions of the low-energy effective theory of the heterotic string.

Observations of neutrino oscillations show that neutrinos have mass. However, the best constraints on this mass currently come from cosmology, via measurements of the cosmic microwave background and large-scale structure. In this paper, we explore the prospects for using low-frequency radio observations of the redshifted 21 cm signal from the epoch of reionization to further constrain neutrino masses. We use the Fisher matrix formalism to compare future galaxy surveys and 21 cm experiments. We show that by pushing to smaller scales and probing a considerably larger volume, 21 cm experiments can provide stronger constraints on neutrino masses than even very large galaxy surveys. Finally, we consider the possibility of going beyond measurements of the total neutrino mass to constraining the mass hierarchies. For a futuristic, 21 cm experiment we show that individual neutrino masses could be measured separately from the total neutrino mass.

There exist full leading-order-in-${\alpha }_{\mathrm{s}}$ numerical calculations of the rates for massless quarks and gluons to split and join in the background of a quark-gluon plasma through hard, nearly collinear bremsstrahlung and inverse bremsstrahlung. In the limit of partons with very high energy $E$, where the physics is dominated by the Landau-Pomeranchuk-Migdal effect, there are also analytic leading-log calculations of these rates, where the logarithm is $\ln (E/T)$. We extend those analytic calculations to next-to-leading-log order. We find agreement with the full result to within roughly 20% for $E_{<}\gtrsim 10T$, where $E_{<}$ is the energy of the least energetic parton in the splitting/joining process. We also discuss how to account for the running of the coupling constant in the case that $E/T$ is very large. Our results are also applicable to isotropic nonequilibrium plasmas if the plasma does not change significantly over the formation time associated with particle splitting.

We expand upon our previous analysis of numerical moving-puncture simulations of the Schwarzschild spacetime. We present a derivation of the family of analytic stationary $1+\log $ foliations of the Schwarzschild solution, and outline a transformation to isotropic coordinates. We discuss in detail the numerical evolution of standard Schwarzschild puncture data, and the new time-independent $1+\log $ data. Finally, we demonstrate that the moving-puncture method can locate the appropriate stationary geometry in a robust manner when a numerical code alternates between two forms of $1+\log $ slicing during a simulation.

Several $f(R)$ modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such $f(R)$ theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of $f(R)$ models.

We show that, within modified gravity, the nonlinear nature of the field equations implies that the usual naïve averaging procedure (replacing the microscopic energy-momentum by its cosmological average) is invalid. We discuss then how the averaging should be performed correctly and show that, as a consequence, at the classical level the physical masses and geodesics of particles, cosmology, and astrophysics in Palatini modified gravity theories are all indistinguishable from the results of general relativity plus a cosmological constant. Palatini gravity is, however, a different theory from general relativity and predicts different internal structures of particles from the latter. On the other hand, and in contrast to classical particles, the electromagnetic field permeates in the space, and hence a different averaging procedure should be applied here. We show that, in general, Palatini gravity theories would then affect the propagation of photons, thus changing the behavior of a Universe dominated by radiation. Finally, Palatini theories also predict alterations to particle physics laws. For example, they can lead to sensitive corrections to the hydrogen energy levels, the measurements of which could be used to place very strong constraints on the properties of viable Palatini gravity theories.

We revisit singularities of two distinct kinds in the Cauchy problem of general scalar-tensor theories of gravity (previously discussed in the literature), and of metric and Palatini $f(R)$ gravity, in both their Jordan and Einstein frame representations. Examples and toy models are used to shed light onto the problem and it is shown that, contrary to common lore, the two conformal frames are equivalent with respect to the initial value problem.

We compute the nonperturbative decay of supersymmetric flat directions due to their $D$-term potential. Flat directions can develop large vacuum expectation values during inflation, and, if they are long-lived, this can strongly affect the reheating and thermalization stages after the inflation. We study a generic system of two $U(1)$ or $SU(2)$ flat directions which are cosmologically evolving after inflation. After proper gauge fixing, we show that the excitations of the fields around this background can undergo exponential amplification, at the expense of the energy density of the flat directions. We compute this effect for several values of the masses and the initial vacuum expectation values of the two flat directions, through a combination of analytical methods and extensive numerical simulations.

We consider stability properties of spherically symmetric spacetimes of stars in metric $f(R)$ gravity. We stress that these not only depend on the particular model, but also on the specific physical configuration. Typically configurations giving the desired ${\gamma }_{\mathrm{PPN}}\approx 1$ are strongly constrained, while those corresponding to ${\gamma }_{\mathrm{PPN}}\approx 1/2$ are less affected. Furthermore, even when the former are found strictly stable in time, the domain of acceptable static spherical solutions typically shrinks to a point in the phase space. Unless a physical reason to prefer such a particular configuration can be found, this poses a naturalness problem for the currently known metric $f(R)$ models for accelerating expansion of the Universe.