We develop a new method of combining cluster observables (number counts and cluster-cluster correlation functions) and stacked weak lensing signals of background galaxy shapes, both of which are available in a wide-field optical imaging survey. Assuming that the clusters have secure redshift estimates, we show that the joint experiment enables a self-calibration of important systematic errors inherent in these measurements, including the source redshift uncertainty and the cluster mass-observable relation, by adopting a single population of background source galaxies for the lensing analysis. The single source galaxy population allows us to use the relative strengths of the stacked lensing signals at different cluster redshifts for calibrating the source redshift uncertainty, which in turn leads to accurate measurements of the mean cluster mass in each redshift and mass bin. In addition, our formulation of the stacked lensing signals in Fourier space simplifies the Fisher matrix calculations, as well as the marginalization over the cluster off-centering effect which is one of the most significant uncertainties in the stacked lensing analysis. We show that upcoming wide-field surveys covering more than a few thousand square degrees yield stringent constraints on cosmological parameters including dark energy parameters, without any priors on nuisance parameters that model systematic uncertainties. Specifically, the stacked lensing information improves the dark energy figure of merit by a factor of 4, compared to that from the cluster observables alone. The primordial non-Gaussianity parameter can also be constrained with a level of $\sigma (f_{\mathrm{NL}})\sim 10$. In this method, the mean source redshift is well calibrated to an accuracy of 0.1 in redshift, and the mean cluster mass in each bin to 5–10% accuracies, which demonstrates the success of the self-calibration of systematic uncertainties from the joint experiment.

The dynamics of general Lovelock gravity, viewed on an arbitrary spherically symmetric surface as a holographic screen, is recast as the form of some generalized first law of thermodynamics on the screen. From this observation together with the other two distinct aspects, where exactly the same temperature and entropy on the screen arise, it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general spherically symmetric screen.

I explore the rich phase diagram of two-flavor QCD as a function of the quark masses. The theory involves three parameters, including one that is $CP$ violating. As the masses vary, regions of both first- and second-order transitions are expected. For nondegenerate quarks, nonperturbative effects cease to be universal, leaving individual quark mass ratios with a renormalization scheme dependence. This raises complications in matching lattice results with perturbative schemes and demonstrates the tautology of attacking the strong $CP$ problem via a vanishing up-quark mass.

Calculable single-sector models provide an elegant framework for generating the flavor textures via compositeness, breaking supersymmetry, and explaining the electroweak scale. Such models may be realized naturally in supersymmetric QCD with additional gauge singlets, though it remains challenging to construct models without a surfeit of light exotic states where the standard model index emerges naturally. We classify possible single-sector models based on $Sp$ confining supersymmetric QCD plus singlets according to their standard model index and number of composite messengers. This leads to simple, calculable models that spontaneously break supersymmetry, reproduce the fermion flavor hierarchy, and explain the standard model index dynamically with little or no additional matter. At low energies these theories realize a “more-minimal” soft spectrum with direct mediation and a gravitino lightest supersymmetric particle.

We demonstrate how most of the light $J^P=0^{+}$ spectrum below 2.0 GeV and their decays can be consistently described by the unitarized quark model incorporating the chiral constraints of Adler zeros and taking $SU(3)$ breaking effects into account. These resonances appear as poles in the complex $s$ plane in a unified picture as $q\overline{q}$ states strongly dressed by hadron loops. Through the large $N_c$ analysis, these resonances are found to naturally separate into two kinds: $\sigma$, $\kappa$, $f_0(980)$, $a_0(980)$ are dynamically generated and run away from the real axis as $N_c$ increases, while the others move towards the $q\overline{q}$ seeds. In this picture, the line shape of $a_0(980)$ is produced by a broad pole below the $K\overline{K}$ threshold, and exhibits characteristics similar to the $\sigma$ and $\kappa$.

The Dalitz plot of ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ decay is studied using $(225.2\pm 2.8)\times {10}^6$ $J/\psi$ events collected with the BESIII detector at the BEPCII $e^{+}{e}^{-}$ collider. With the largest sample of ${\eta }^{\prime }$ decays to date, the parameters of the Dalitz plot are determined in a generalized and a linear representation. Also, the branching fraction of $J/\psi \to \gamma {\eta }^{\prime }$ is determined to be $(4.84\pm 0.03\pm 0.24)\times {10}^{-3}$, where the first error is statistical and the second systematic.

We report on a search for new particles in the diphoton channel using a data sample of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the CDF II detector at the Fermilab Tevatron, with an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$. The diphoton invariant mass spectrum of the data agrees well with the standard model expectation. We set upper limits on the production cross section times branching ratio for the Randall-Sundrum graviton, as a function of diphoton mass. We subsequently derive lower limits on the graviton mass of $459\mathrm{GeV}/c^2$ and $963\mathrm{GeV}/c^2$, at the 95% confidence level, for coupling parameters ($k/{\overline{M}}_{\mathrm{Pl}}$) of 0.01 and 0.1, respectively.

Measurement of the CMB bispectrum, or three-point correlation function, has now become one of the principle efforts in early-Universe cosmology. Here we show that there is an odd-parity component of the CMB bispectrum that has been hitherto unexplored. We argue that odd-parity temperature-polarization bispectra can arise, in principle, through weak lensing of the CMB by chiral gravitational waves or through cosmological birefringence, although the signals will be small even in the best-case scenarios. Measurement of these bispectra requires only modest modifications to the usual data-analysis algorithms. They may be useful as a consistency test in searches for the usual bispectrum and to search for surprises in the data.

In this paper we apply the equation of state (EOS) of QCD at finite chemical potential and zero temperature proposed in H. S. Zong and W. M. Sun [Int. J. Mod. Phys. A 23, 3591 (2008)] to the study of properties of quark star. This EOS contains only one adjustable parameter $m_D$ which sets the scale of chiral symmetry breaking (in our calculation we have chosen two values of $m_D$: $m_D=244\mathrm{MeV}$ and $m_D=239\mathrm{MeV}$, which is fitted from the value of $f_{\pi }$ and determined by $e^{+}{e}^{-}$ annihilation experiment, respectively). From this EOS a model of quark star is established by applying the Tolman-Oppenheimer-Volkoff equation under two conditions: with the $P(\mu =0)$ term and without the $P(\mu =0)$ term. Our results show clearly that the $P(\mu =0)$ term is an important quantity in the study of quark star. A comparison between our model and other models of quark star is made. In particular, we have compared our results with the most recent observational data measured using Shapiro delay reported in P. B. Demorest et al. [Nature (London) 467, 1081 (2010)].

We investigate the quantum kinetic approach to pair production from vacuum by a time-dependent electric field. Equivalence between this approach and the more familiar $S$-matrix approach is explicitly established for both scalar and fermion cases. For the particular case of a constant electric field, the exact solution for kinetic equations is provided and the accuracy of low-density approximation is estimated.

To model the radiative evolution of extreme mass-ratio binary inspirals (a key target of the LISA mission), the community needs efficient methods for computation of the gravitational self-force (SF) on the Kerr spacetime. Here we further develop a practical “$m$-mode regularization” scheme for SF calculations, and give the details of a first implementation. The key steps in the method are (i) removal of a singular part of the perturbation field with a suitable “puncture” to leave a sufficiently regular residual within a finite worldtube surrounding the particle’s worldline, (ii) decomposition in azimuthal ($m$) modes, (iii) numerical evolution of the $m$ modes in $2+1\mathrm{D}$ with a finite-difference scheme, and (iv) reconstruction of the SF from the mode sum. The method relies on a judicious choice of puncture, based on the Detweiler-Whiting decomposition. We give a working definition for the “order” of the puncture, and show how it determines the convergence rate of the $m$-mode sum. The dissipative piece of the SF displays an exponentially convergent mode sum, while the $m$-mode sum for the conservative piece converges with a power law. In the latter case, the individual modal contributions fall off at large $m$ as $m^{-n}$ for even $n$ and as $m^{-n+1}$ for odd $n$, where $n$ is the puncture order. We describe an $m$-mode implementation with a 4th-order puncture to compute the scalar-field SF along circular geodesics on Schwarzschild. In a forthcoming companion paper we extend the calculation to the Kerr spacetime.

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order “Killing spinor” equation in “fake supergravity” coupled to arbitrary $U(1)$ gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial “Killing spinor,” which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting $M2$/$M2$/$M2$-branes in a rotating Kasner universe. The Kaluza-Klein–type black holes are also discussed.

After recalling the concept of the Hausdorff dimension, we study the fractal properties of a quantum particle path. As a novelty we consider the possibility for the space where the particle propagates to be endowed with a quantum-gravity-induced minimal length. We show that the Hausdorff dimension accounts for both the quantum mechanics uncertainty and manifold fluctuations. In addition the presence of a minimal length breaks the self-similarity property of the erratic path of the quantum particle. Finally we establish a universal property of the Hausdorff dimension as well as the spectral dimension: They both depend on the amount of resolution loss which affects both the path and the manifold when quantum gravity fluctuations occur.

We study charged particle motion in weakly charged higher dimensional black holes. To describe the electromagnetic field we use a test field approximation and the higher dimensional Kerr-NUT-(A)dS metric as a background geometry. It is shown that for a special configuration of the electromagnetic field, the equations of motion of charged particles are completely integrable. The vector potential of such a field is proportional to one of the Killing vectors (called a primary Killing vector) from the “Killing tower” of symmetry generating objects which exists in the background geometry. A free constant in the definition of the adopted electromagnetic potential is proportional to the electric charge of the higher dimensional black hole. The full set of independent conserved quantities in involution is found. We demonstrate that Hamilton-Jacobi equations are separable, as is the corresponding Klein-Gordon equation and its symmetry operators.

We study the production, spectrum, and detectability of gravitational waves in models of the early Universe where first order phase transitions occur during inflation. We consider all relevant sources. The self-consistency of the scenario strongly affects the features of the waves. The spectrum appears to be mainly sourced by collisions of bubble of the new phases, while plasma dynamics (turbulence) and the primordial gauge fields connected to the physics of the transitions are generally subdominant. The amplitude and frequency dependence of the spectrum for modes that exit the horizon during inflation are different from those of the waves produced by quantum vacuum oscillations of the metric or by first order phase transitions not occurring during inflation. A not too large number of slow (but still successful) phase transitions can leave detectable marks in the common microwave background radiation, but the signal weakens rapidly for faster transitions. When the number of phase transitions is instead large, the primordial gravitational waves can be observed both in the common microwave background radiation or with LISA (but in this case only marginally, for the slowest transitions) and especially with DECIGO. We also discuss the nucleosynthesis bound and the constraints it places on the parameters of the models.

Assuming homogeneous isotropic $\Lambda \mathrm{CDM}$ cosmology allows $\Lambda$, spatial curvature, and dark matter density to be inferred from large scale structure observations such as supernovae. The purpose of this paper is to extend this to allow observations to measure or constrain inhomogeneity and anisotropy. We obtain the general inhomogeneous anisotropic $\Lambda \mathrm{CDM}$ solution which is locally asymptotic to an expanding de Sitter solution as a late time expansion using Starobinsky’s method (analogous to the “holographic renormalization” technique in AdS/CFT) together with a resummation of the expansion. The dark matter is modeled as perfect dust fluid. The terms in the expansion systematically describe inhomogeneous and anisotropic deformations of an expanding Friedmann-Lemaître-Robertson-Walker solution and are given as a spatial derivative expansion in terms of data characterizing the solution—a 3-metric and a perturbation of that 3-metric. Leading terms describe inhomogeneity and anisotropy on the scale set by the cosmological constant, approximately the horizon scale today. Higher terms in the expansion describe shorter scale variations. We compute the luminosity-distance-redshift relation and argue that comparison with current and future observations would allow a partial reconstruction of the characterizing data. We also comment on smoothing these solutions noting that geometric flows (such as Ricci flow) applied to the characterizing data provide a canonical smoothing method.

We present a scenario in which a scalar field dark energy is coupled to the trace of the energy momentum tensor of the baryonic matter fields. In the slow-roll regime, this interaction could give rise to the cosmological features of dark matter. We work out the cosmological background solutions and fit the parameters of the model using the Union 2 supernovae data set. Then, we develop cosmological perturbations up to linear order, and we find that the perturbed variables have an acceptable behavior, in particular, the density contrast of baryonic matter grows similar to that in the $\Lambda \mathrm{CDM}$ model for a suitable choice of the strength parameter of the coupling.

Minimum-variance estimators for the parameter $f_{\mathrm{nl}}$ that quantifies local-model non-Gaussianity can be constructed from the cosmic microwave background (CMB) bispectrum (three-point function) and also from the trispectrum (four-point function). Some have suggested that a comparison between the estimates for the values of $f_{\mathrm{nl}}$ from the bispectrum and trispectrum allow a consistency test for the model. But others argue that the saturation of the Cramer-Rao bound—which gives a lower limit to the variance of an estimator—by the bispectrum estimator implies that no further information on $f_{\mathrm{nl}}$ can be obtained from the trispectrum. Here, we elaborate the nature of the correlation between the bispectrum and trispectrum estimators for $f_{\mathrm{nl}}$. We show that the two estimators become statistically independent in the limit of large number of CMB pixels, and thus that the trispectrum estimator does indeed provide additional information on $f_{\mathrm{nl}}$ beyond that obtained from the bispectrum. We explain how this conclusion is consistent with the Cramer-Rao bound. Our discussion of the Cramer-Rao bound may be of interest to those doing Fisher-matrix parameter-estimation forecasts or data analysis in other areas of physics as well.

Primordial magnetic fields present since before the epoch of matter-radiation equality have an effect on the anisotropies of the cosmic microwave background (CMB). The CMB anisotropies due to scalar perturbations are calculated in the gauge-invariant formalism for magnetized adiabatic initial conditions. Furthermore, the linear matter power spectrum is calculated. Numerical solutions are complemented by a qualitative analysis.