Using the general structure of the vacuum polarization tensor ${\Pi }_{\mu \nu }(k_0,\mathbf{k})$ in the infrared (IR) limit, $k_0\to 0$, the ring contribution to the QED effective potential at finite temperature and the nonzero magnetic field is determined beyond the static limit, ($k_0\to 0$, $\mathbf{k}\to \mathbf{0}$). The resulting ring potential is then studied in weak and strong magnetic field limits. In the weak magnetic field limit, at high temperature and for $\alpha \to 0$, the improved ring potential consists of a term proportional to $T^4{\alpha }^{5/2}$, in addition to the expected $T^4{\alpha }^{3/2}$ term arising from the static limit. Here, $\alpha$ is the fine structure constant. In the limit of the strong magnetic field, where QED dynamics is dominated by the lowest Landau level, the ring potential includes a novel term consisting of dilogarithmic function $(eB){\mathrm{Li}}_2(-\frac{2\alpha }{\pi }\frac{eB}{m^2})$. Using the ring improved (one-loop) effective potential including the one-loop effective potential and ring potential in the IR limit, the dynamical chiral symmetry breaking of QED is studied at finite temperature and in the presence of the strong magnetic field. The gap equation, the dynamical mass and the critical temperature of QED in the regime of the lowest Landau level dominance are determined in the improved IR as well as in the static limit. For a given value of the magnetic field, the improved ring potential is shown to be more efficient in decreasing the critical temperature arising from the one-loop effective potential.

We present a kind of generalized Vaidya solutions in a generic Lovelock gravity. This solution generalizes the simple case in Gauss-Bonnet gravity reported recently by some authors. We study the thermodynamics of apparent horizon in this generalized Vaidya spacetime. Treating those terms except for the Einstein tensor as an effective energy-momentum tensor in the gravitational field equations, and using the unified first law in Einstein gravity theory, we obtain an entropy expression for the apparent horizon. We also obtain an energy expression of this spacetime, which coincides with the generalized Misner-Sharp energy proposed by Maeda and Nozawa in Lovelock gravity.

We report on our code, in which the moving puncture method is applied and an adaptive/fixed mesh refinement is implemented, and on its preliminary performance on black hole simulations. Based on the Baumgarte-Sharpiro-Shibata-Nakamura (BSSN) formulation, up-to-date gauge conditions and the modifications of the formulation are also implemented and tested. In this work, we present our primary results about the simulation of a single static black hole, of a moving single black hole, and of the head-on collision of a binary black hole system. For the static punctured black hole simulations, different modifications of the BSSN formulation are applied. It is demonstrated that both the currently used sets of modifications lead to a stable evolution. For cases of a moving punctured black hole with or without spin, we search for viable gauge conditions and study the effect of spin on the black hole evolution. Our results confirm previous results obtained by other research groups. In addition, we find a new gauge condition, which has not yet been adopted by any other researchers, which can also give stable and accurate black hole evolution calculations. We examine the performance of the code for the head-on collision of a binary black hole system, and the agreement of the gravitational waveform it produces with that obtained in other works. In order to understand qualitatively the influence of matter on the binary black hole collisions, we also investigate the same head-on collision scenarios but perturbed by a scalar field. The numerical simulations performed with this code not only give stable and accurate results that are consistent with the works by other numerical relativity groups, but also lead to the discovery of a new viable gauge condition, as well as clarify some ambiguities in the modification of the BSSN formulation. These results demonstrate that this code is reliable and ready to be used in the study of more realistic astrophysical scenarios and of numerical relativity.

We consider here a manifestly covariant quark model of the nucleon and the $\Delta$, where one quark is off shell, and the other two quarks form an on-shell diquark pair. Using this model, we have shown previously that the nucleon form factors and the dominant form factor for the $\gamma N\to \Delta$ transition (the magnetic dipole (M1) form factor) can be well described by nucleon and $\Delta$ wave functions with S-state components only. In this paper, we show that nonvanishing results for the small electric (E2) and Coulomb (C2) quadrupole form factors can be obtained if D-state components are added to the $\Delta$ valence quark wave function. We present a covariant definition of these components and compute their contributions to the form factors. We find that these components cannot, by themselves, describe the data. Explicit pion cloud contributions must also be added, and these contributions dominate both the E2 and the C2 form factors. By parametrizing the pion cloud contribution for the transition electric and Coulomb form factors in terms of the neutron electric form factor, we estimate that the contributions of the $\Delta$ D-state coupled to quark core spin of $3/2$ is of the order of 1%, and the contributions of the $\Delta$ D-state coupled to quark core spin $1/2$ is of the order of 4%.

The equilibration of matter and onset of hydrodynamics can be understood in the AdS/CFT context as a gravitational collapse process, in which “collision debris” create a horizon. In this paper we consider the simplest geometry possible, a flat shell (or membrane) falling in the holographic direction toward the horizon. The metric is a combination of two well-known solutions: thermal AdS above the shell and pure AdS below, while motion of the shell is given by the Israel junction condition. Furthermore, when the shell motion can be considered slow, we were able to solve for two-point functions of all boundary stress tensors and found that an observer on the boundary sees a very peculiar quasiequilibrium: while the average stress tensor $<T_{\mu \nu >}$ contains the equilibrium plasma energy and pressure at all times, the spectral densities of the correlators (related with occupation probabilities of the modes) reveal additional oscillating terms absent in equilibrium. This is explained by the echo phenomenon, a partial return of the field coherence at certain echo times.

It is shown that under essentially all conditions, the nonlinear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial metric divided by the square of the Robertson–Walker scale factor $a$) is time independent, though with an arbitrary dependence on comoving coordinates, and all perturbations to the other metric components and to all matter variables vanish, to leading order in $1/a$. The corrections are of order $1/a^2$, and are explicitly given for the reduced metric in a multifield model with a general potential. Further, this is the solution that describes the metric and matter produced by single-field inflation. These results justify the use of observed non-Gaussian correlations (or their absence) as a test of theories of single-field inflation, despite our ignorance of the constituents of the Universe while fluctuations are outside the horizon after inflation, as long as graphs with loops can be neglected.

Measurements of cosmic microwave background temperature fluctuations by the Wilkinson Microwave Anisotropy Probe indicate that the fluctuation amplitude in one half of the sky differs from the amplitude in the other half. We show that such an asymmetry cannot be generated during single-field slow-roll inflation without violating constraints to the homogeneity of the Universe. In contrast, a multifield inflationary theory, the curvaton model, can produce this power asymmetry without violating the homogeneity constraint. The mechanism requires the introduction of a large-amplitude superhorizon perturbation to the curvaton field, possibly a preinflationary remnant or a superhorizon curvaton-web structure. The model makes several predictions, including non-Gaussianity and modifications to the inflationary consistency relation, that will be tested with forthcoming cosmic microwave background experiments.

We consider the generation of gravitational waves by primordial helical inverse-cascade magnetohydrodynamic (MHD) turbulence produced by bubble collisions at the electroweak phase transition. We extend the previous study [1] by considering both currently discussed models of MHD turbulence. For popular electroweak phase transition parameter values, the generated gravitational wave spectrum is only weakly dependent on the MHD turbulence model. Compared with the unmagnetized electroweak phase transition case, the spectrum of MHD-turbulence-generated gravitational waves peaks at lower frequency with larger amplitude and can be detected by the proposed Laser Interferometer Space Antenna.

We consider models of light superweakly interacting cold dark matter, with $\mathcal{O}(10–100)\mathrm{keV}$ mass, focusing on bosonic candidates such as pseudoscalars and vectors. We analyze the cosmological abundance, the $\gamma$ background created by particle decays, the impact on stellar processes due to cooling, and the direct-detection capabilities in order to identify classes of models that pass all the constraints. In certain models, variants of photoelectric (or axioelectric) absorption of dark matter in direct-detection experiments can provide a sensitivity to the superweak couplings to the standard model which is superior to all existing indirect constraints. In all models studied, the annual modulation of the direct-detection signal is at the currently unobservable level of $O({10}^{-5})$.

Simple supersymmetric SO(10) grand unified theory in five dimensions is proposed, in which the fifth dimension is compactified on the $S^1/(Z_2\times Z_2^{\prime })$ orbifold with two inequivalent branes at the orbifold fixed points. In this model, all matter and Higgs multiplets reside on one brane (PS brane) where the Pati-Salam (PS) symmetry is manifest, while only the SO(10) gauge multiplet resides on the bulk. The supersymmetry breaking on the other brane [SO(10) brane] is transmitted to the PS brane through the gaugino mediation with the bulk gauge multiplet. We examine sparticle mass spectrum in this setup and show that the neutralino LSP as the dark matter candidate can be realized when the compactification scale of the fifth dimension is higher than the PS symmetry breaking scale, keeping the successful gauge coupling unification after incorporating threshold corrections of Kaluza-Klein modes of the bulk gauge multiplets.

We revisit the earlier determination of ${\alpha }_s(M_Z)$ via perturbative analyses of short-distance-sensitive lattice observables, incorporating new lattice data and performing a modified version of the original analysis. We focus on two high-intrinsic-scale observables, $\log (W_{11})$ and $\log (W_{12})$, and one lower-intrinsic-scale observable, $\log (W_{12}/u_0^6)$, finding improved consistency among the values extracted using the different observables and a final result, ${\alpha }_s(M_Z)=0.1192\pm 0.0011$, $\sim 2\sigma$ higher than the earlier result, in excellent agreement with recent nonlattice determinations and, in addition, in good agreement with the results of a similar, but not identical, reanalysis by the HPQCD Collaboration. A discussion of the relation between the two reanalyses is given, focusing on the complementary aspects of the two approaches.

We construct a novel topologically massive Abelian Chern-Simons gauge theory with 32 global supersymmetries in three space-time dimensions. In spite of the 32 supercharges, the theory exhibits massive excitations only up to spin 1. The possibility of such a multiplet shortening is due to the presence of noncentral R-symmetry generators in the Poincaré superalgebra, whose supermultiplets are determined.

We show that gravity cures the infrared divergence of the Yang monopole when a proper definition of conserved quantities in curved backgrounds is used, i.e. the gravitating Yang monopole in cosmological Einstein theory has a finite mass in generic even dimensions (including time). In addition, we find exact Yang-monopole type solutions in the cosmological Einstein-Gauss-Bonnet-Yang-Mills theory and briefly discuss their properties.

I compute the effect on the power spectrum of tracers of the large-scale mass-density field (e.g., galaxies) of primordial non-Gaussianity of the form $\Phi =\varphi +f_{\mathrm{NL}}({\varphi }^2-⟨{\varphi }^2⟩)+g_{\mathrm{NL}}{\varphi }^3+\dots$, where $\Phi$ is proportional to the initial potential fluctuations and $\varphi$ is a Gaussian field, using beyond-linear-order perturbation theory. I find that the need to eliminate large higher-order corrections necessitates the addition of a new term to the bias model, proportional to $\varphi$, i.e., ${\delta }_g=b_{\delta }\delta +b_{\varphi }{f}_{\mathrm{NL}}\varphi +\dots$, with all the consequences this implies for clustering statistics, e.g., $P_{gg}(k)=b_{\delta }^2{P}_{\delta \delta }(k)+2b_{\delta }{b}_{\varphi }{f}_{\mathrm{NL}}{P}_{\varphi \delta }(k)+b_{\varphi }^2{f}_{\mathrm{NL}}^2{P}_{\varphi \varphi }(k)+\dots$. This result is consistent with calculations based on a model for dark matter halo clustering, showing that the form is quite general, not requiring assumptions about peaks, or the formation or existence of halos. The halo model plays the same role it does in the usual bias picture, giving a prediction for $b_{\varphi }$ for galaxies known to sit in a certain type of halo. Previous projections for future constraints based on this effect have been very conservative—there is enough volume at $z\lesssim 2$ to measure $f_{\mathrm{NL}}$ to $\sim \pm 1$, with much more volume at higher $z$. As a prelude to the bias calculation, I point out that the beyond-linear (in $\varphi$) corrections to the power spectrum of mass-density perturbations are naively infinite, so it is dangerous to assume they are negligible; however, the infinite part can be removed by a renormalization of the fluctuation amplitude, with the residual $k$-dependent corrections negligible for models allowed by current constraints.

I recently proposed the “reheating-volume” (RV) prescription as a possible solution to the measure problem in “multiverse” cosmology. The goal of this work is to extend the RV measure to scenarios involving bubble nucleation, such as the string theory landscape. In the spirit of the RV prescription, I propose to calculate the distribution of observable quantities in a landscape that is conditioned in probability to nucleate a finite total number of bubbles to the future of an initial bubble. A general formula for the relative number of bubbles of different types can be derived. I show that the RV measure is well defined and independent of the choice of the initial bubble type, as long as that type supports further bubble nucleation. Applying the RV measure to a generic landscape, I find that the abundance of Boltzmann brains is always negligibly small compared with the abundance of ordinary observers in the bubbles of the same type. As an illustration, I present explicit results for a toy landscape containing four vacuum states, and for landscapes with a single high-energy vacuum and a large number of low-energy vacua.

Galaxy-galaxy or galaxy-quasar lensing can provide important information on the mass distribution in the Universe. It consists of correlating the lensing signal (either shear or magnification) of a background galaxy/quasar sample with the number density of a foreground galaxy sample. However, the foreground galaxy density is inevitably altered by the magnification bias due to the mass between the foreground and the observer, leading to a correction to the observed galaxy-lensing signal. The aim of this paper is to quantify this correction. The single most important determining factor is the foreground redshift $z_f$: the correction is small if the foreground galaxies are at low redshifts but can become non-negligible for sufficiently high redshifts. For instance, we find that for the multipole $\ell =1000$, the correction is above $1\%\times (5s_f-2)/b_f$ for $z_f\gtrsim 0.37$, and above $5\%\times (5s_f-2)/b_f$ for $z_f\gtrsim 0.67$, where $s_f$ is the number count slope of the foreground sample and $b_f$ its galaxy bias. These considerations are particularly important for geometrical measures, such as the Jain and Taylor ratio or its generalization by Zhang et al. Assuming $(5s_f-2)/b_f=1$, we find that the foreground redshift should be limited to $z_f\lesssim 0.45$ in order to avoid biasing the inferred dark energy equation of state $w$ by more than 5%, and that even for a low foreground redshift ($<0.45$), the background samples must be well separated from the foreground to avoid incurring a bias of similar magnitude. Lastly, we briefly comment on the possibility of obtaining these geometrical measures without using galaxy shapes, using instead magnification bias itself.

The transverse distribution of gluon and quark-antiquark pairs produced from a strong constant chromoelectric field depends on two gauge invariant quantities, $C_1=E^a{E}^a$ and $C_2=[d_{abc}{E}^a{E}^b{E}^c{]}^2$, as shown earlier in [G. C. Nayak and P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005)] for gluons and in [G. C. Nayak, Phys. Rev. D 72, 125010 (2005)] for quarks. Here, we discuss the explicit dependence of the distribution on the second Casimir invariant $C_2$ and show the dependence is at most a 15% effect.

Using recent precise hadronic $\tau$-decay data on the $V-A$ spectral function, and general properties of QCD such as analyticity, the operator product expansion, and chiral perturbation theory, we get accurate values for the QCD chiral order parameters $L_{10}^r(M_{\rho })$ and $C_{87}^r(M_{\rho })$. These two low-energy constants appear at order $p^4$ and $p^6$, respectively, in the chiral perturbation theory expansion of the $V-A$ correlator. At order $p^4$ we obtain $L_{10}^r(M_{\rho })=-(5.22\pm 0.06)\times {10}^{-3}$. Including in the analysis the two-loop (order $p^6$) contributions, we get $L_{10}^r(M_{\rho })=-(4.06\pm 0.39)\times {10}^{-3}$ and $C_{87}^r(M_{\rho })=(4.89\pm 0.19)\times {10}^{-3}{\mathrm{GeV}}^{-2}$. In the SU(2) chiral effective theory, the corresponding low-energy coupling takes the value ${\overline{l}}_5=13.30\pm 0.11$ at order $p^4$, and ${\overline{l}}_5=12.24\pm 0.21$ at order $p^6$.