We propose a novel method for the effective action of spinor and scalar QED at finite temperature in time-dependent electric fields, where charged pairs evolve in a nonadiabatic way. The imaginary part of the effective action consists of thermal loops of the Fermi-Dirac or Bose-Einstein distribution for the initial thermal ensemble, weighted with factors of the Bogoliubov coefficients for quantum effects. And the real part of the effective action is determined by the mean number of produced pairs and vacuum polarization at zero temperature. In the weak-field limit, the mean number of produced pairs is shown twice the imaginary part. We explicitly find the finite-temperature effective action in a constant electric field.

We find the Bogoliubov coefficient from the tunneling boundary condition on charged particles in a static electric field $E_0{\mathrm{sech}}^2(z/L)$ and, using the regularization scheme in Phys. Rev. D 78, 105013 (2008), obtain the exact one-loop effective action in scalar and spinor QED. It is shown that the effective action satisfies the general relation between the vacuum persistence and the mean number of produced pairs. We advance an approximation method for general electric fields and show the duality between the space-dependent and time-dependent electric fields of the same form at the leading order of the effective actions.

We investigate the propagation and evolution for a massless scalar field in the background of $\lambda =1/2$ Hořava-Lifshitz black hole with the condition of detailed balance. We fortunately obtain an exact solution for the Klein-Gordon equation. Then, we find an analytical expression for the greybody factor which is valid for any frequency and also exactly show that the perturbation decays without any oscillation. All of these can help us to understand more about the Hořava-Lifshitz gravity.

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f(R,\varphi ,X)/2+{\mathcal{L}}_c$, where $R$ is a Ricci scalar, $\varphi$ is a scalar field, and $X=-{\partial }^{\mu }\varphi {\partial }_{\mu }\varphi /2$ is a field kinetic energy. We take into account a nonlinear self-interaction term ${\mathcal{L}}_c=\xi (\varphi )\square \varphi ({\partial }^{\mu }\varphi {\partial }_{\mu }\varphi )$ recently studied in the context of “Galileon” cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasistatic approximation on subhorizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature; and thus it is convenient to test the viability of such models from both theoretical and observational points of view.

Cosmological backreaction suggests a link between structure formation and the expansion history of the Universe. In order to quantitatively examine this connection, we dynamically investigate a volume partition of the Universe into over- and underdense regions. This allows us to trace structure formation using the volume fraction of the overdense regions ${\lambda }_{\mathcal{M}}$ as its characterizing parameter. Employing results from cosmological perturbation theory and extrapolating the leading mode into the nonlinear regime, we construct a three-parameter model for the effective cosmic expansion history, involving ${\lambda }_{{\mathcal{M}}_0}$, the matter density ${\Omega }_m^{{\mathcal{D}}_0}$, and the Hubble rate $H_{{\mathcal{D}}_0}$ of today’s Universe. Taking standard values for ${\Omega }_m^{{\mathcal{D}}_0}$ and $H_{{\mathcal{D}}_0}$ as well as a reasonable value for ${\lambda }_{{\mathcal{M}}_0}$, that we derive from $N$-body simulations, we determine the corresponding amounts of backreaction and spatial curvature. We find that the obtained values that are sufficient to generate today’s structure also lead to a $\Lambda \mathrm{CDM}$-like behavior of the scale factor, parametrized by the same parameters ${\Omega }_m^{{\mathcal{D}}_0}$ and $H_{{\mathcal{D}}_0}$, but without a cosmological constant. However, the temporal behavior of ${\lambda }_{\mathcal{M}}$ does not faithfully reproduce the structure formation history. Surprisingly, however, the model matches with structure formation with the assumption of a low matter content, ${\Omega }_m^{{\mathcal{D}}_0}\approx 3\%$, a result that hints to a different interpretation of part of the backreaction effect as kinematical dark matter. A complementary investigation assumes the $\Lambda \mathrm{CDM}$ fit-model for the evolution of the global scale factor by imposing a global replacement of the cosmological constant through backreaction, and also supposes that a Newtonian simulation of structure formation provides the correct volume partition into over- and underdense regions. From these assumptions we derive the corresponding evolution laws for backreaction and spatial curvature on the partitioned domains. We find the correct scaling limit predicted by perturbation theory, which allows us to rederive higher-order results from perturbation theory on the evolution laws for backreaction and curvature analytically. This strong backreaction scenario can explain structure formation and dark energy simultaneously. We conclude that these results represent a conceptually appealing approach towards a solution of the dark energy and coincidence problems. Open problems are the still too large amplitude of initial perturbations that are required for the scenarios proposed, and the role of dark matter that may be partially taken by backreaction effects. Both drawbacks point to the need of a reinterpretation of observational data in the new framework.

One of the most promising ways of detecting primordial gravitational waves generated during inflation is to observe $B$-modes of polarization, generated by Thomson scattering after reionization, in the cosmic microwave background. Large scale foregrounds though are expected to be a major systematic issue, so—in the event of a tentative detection—an independent confirmation of large scale gravitational waves would be almost essential. Previous authors have suggested searching for the analogous mode of cosmic shear in weak lensing surveys but have shown that the signal to noise of this mode is marginal at best. This argument is reconsidered here, accounting for the cross correlations of the polarization and lensing $B$-modes. A lensing survey can potentially strengthen the argument for a detection of primordial gravitational waves, although it is unlikely to help constrain the amplitude of the signal.

We reexamine the constraints on the cosmic string tension from cosmic microwave background (CMB) and matter power spectra, and also from limits on a stochastic background of gravitational waves provided by pulsar timing. We discuss the different approaches to modeling string evolution and radiation. In particular, we show that the unconnected segment model can describe CMB spectra expected from thin string (Nambu) and field theory (Abelian-Higgs) simulations using the computed values for the correlation length, rms string velocity and small-scale structure relevant to each variety of simulation. Applying the computed spectra in a fit to CMB and SDSS data we find that $G\mu /c^2<2.6\times {10}^{-7}$ ($2\sigma$) if the Nambu simulations are correct and $G\mu /c^2<6.4\times {10}^{-7}$ in the Abelian-Higgs case. The degeneracy between $G\mu /c^2$ and the power spectrum slope $n_{\mathrm{S}}$ is substantially reduced from previous work. Inclusion of constraints on the baryon density from big bang nucleosynthesis (BBN) imply that $n_{\mathrm{S}}<1$ at around the $4\sigma$ level for both the Nambu and Abelian-Higgs cases. As a by-product of our results, we find there is “moderate-to-strong” Bayesian evidence that the Harrison-Zel’dovich spectrum is excluded (odds ratio of $\sim 100:1$) by the combination of CMB, SDSS, and BBN when compared to the standard 6 parameter fit. Using the contribution to the gravitational wave background from radiation era loops as a conservative lower bound on the signal for specific values of $G\mu /c^2$ and loop production size, $\alpha$, we find that $G\mu /c^2<7\times {10}^{-7}$ for $\alpha c^2/(\Gamma G\mu )\ll 1$ and $G\mu /c^2<5\times {10}^{-11}/\alpha$ for $\alpha c^2/(\Gamma G\mu )\gg 1$.

It is becoming crucial to understand orbital-angular-momentum contributions for clarifying the nucleon-spin issue in the parton level. Twist-two structure functions $b_1$ and $b_2$ for spin-one hadrons could probe orbital-angular-momentum effects, which reflect a different aspect from current studies for the spin-$1/2$ nucleon. The structure functions $b_1$ and $b_2$ are described by tensor-polarized quark and antiquark distributions ${\delta }_{T}q$ and ${\delta }_T\overline{q}$. Using HERMES data on the $b_1$ structure function for the deuteron, we made an analysis of extracting the distributions ${\delta }_{T}q$ and ${\delta }_T\overline{q}$ in a simple $x$-dependent functional form. Optimum distributions are proposed for the tensor-polarized valence and antiquark distribution functions from the analysis. A finite tensor polarization is obtained for antiquarks if we impose a constraint that the first moments of tensor-polarized valence-quark distributions vanish.

We derive nonlinear recursion equations for the leading infrared logarithms in massless nonrenormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.

We construct line shapes for the $X(3872)$, which generalize the Flatté and zero-range line shapes that have been considered previously. These line shapes are associated with scattering amplitudes that are exactly unitary for real values of the interaction parameters and can be derived from a renormalizable quantum field theory. The new line shapes can be used to discriminate between the alternative binding mechanisms in which the $X(3872)$ is generated either dynamically by charm-meson interactions or by a resonance near the $D^{*0}{\overline{D}}^0$ threshold. If the resonance is identified with the $P$-wave charmonium state ${\chi }_{c1}^{\prime }$, the interaction parameters can be constrained by using charmonium phenomenology. We analyze data on the $X(3872)$ and also data from the Belle and BABAR Collaborations on the invariant mass distribution of the charm mesons from the decay $B\to K+D^{*0}{\overline{D}}^0$ up to 4000 MeV. Our analysis is compatible with the mechanism for the $X(3872)$ being either a fine-tuning of charm-meson interactions or the fine-tuning of the ${\chi }_{c1}^{\prime }$ to the $D^{*0}{\overline{D}}^0$ threshold. In particular, the data do not exclude a separate ${\chi }_{c1}^{\prime }$ resonance between the $D^{*+}{D}^{-}$ threshold and 4000 MeV.

We study the thermal leptogenesis in a hybrid model, which combines the so-called split fermion model and the bulk neutrino model defined in five-dimensional spacetime. This model predicts the existence of a heavy neutrino pair nearly degenerate in mass, whose decays might generate a $CP$ violation large enough for creating the baryon asymmetry of the Universe through leptogenesis. We investigate numerically the constraints this sets on the parameters of the model such as the size of the compactified fifth dimension.

We have performed a search for $CP$ violation in a sample of $B_s^0\to {\mu }^{+}{D}_s^{-}X$ decays corresponding to $5{\mathrm{fb}}^{-1}$ of proton-antiproton collisions collected by the D0 detector in Run II at the Fermilab Tevatron Collider. New physics in $B_s^0$ mixing could contribute a significant $CP$ violating weak phase, which would be observed as a difference in the decay-time distribution for $B_s^0\to {\overline{B}}_s^0$ oscillated states versus that for ${\overline{B}}_s^0\to B_s^0$. A fit to the decay-time distributions of the $B_s^0/{\overline{B}}_s^0$ candidates yields the flavor-specific asymmetry $a_{\mathrm{fs}}^s=[-1.7\pm 9.1(\mathrm{stat}{)}_{-1.5}^{+1.4}(\mathrm{syst})]\times {10}^{-3}$, which excludes $CP$ violation due to new physics within the experimental sensitivity.

The compatibility of higher-order Laguerre-Gauss (LG) modes with interferometric technologies commonly used in gravitational wave detectors is investigated. In this paper, we present the first experimental results concerning the performance of the ${\mathrm{LG}}_{33}$ mode in optical resonators. We show that the Pound-Drever-Hall error signal for a ${\mathrm{LG}}_{33}$ mode in a linear optical resonator is identical to that of the more commonly used ${\mathrm{LG}}_{00}$ mode, and demonstrate the feedback control of the resonator with a ${\mathrm{LG}}_{33}$ mode. We succeeded to increase the mode purity of a ${\mathrm{LG}}_{33}$ mode generated using a spatial-light modulator from 51% to 99% upon transmission through a linear optical resonator. We further report the experimental verification that a triangular optical resonator does not transmit helical LG modes.

Employing higher order perturbation theory, we obtain charged rotating black holes in odd dimensions, where the Einstein-Maxwell Lagrangian may be supplemented with a Chern-Simons term. Starting from the Myers-Perry solutions, we use the electric charge as the perturbative parameter and focus on extremal black holes with equal-magnitude angular momenta. For Einstein-Maxwell-Chern-Simons theory with arbitrary Chern-Simons coupling constant, we perform the perturbations up to 3rd order for any odd dimension. We discuss the physical properties of these black holes and study their dependence on the charge. In particular, we show that the gyromagnetic ratio $g$ of Einstein-Maxwell black holes differs from the lowest order perturbative value $D-2$, and that the first correction term to $g/(D-2)$ is universal.

A quasiblack hole is an object in which its boundary is situated at a surface called the quasihorizon, defined by its own gravitational radius. We elucidate under which conditions a quasiblack hole can form under the presence of matter with nonzero pressure. It is supposed that in the outer region an extremal quasihorizon forms, whereas inside, the quasihorizon can be either nonextremal or extremal. It is shown that in both cases, nonextremal or extremal inside, a well-defined quasiblack hole always admits a continuous pressure at its own quasihorizon. Both the nonextremal and extremal cases inside can be divided into two situations, one in which there is no electromagnetic field, and the other in which there is an electromagnetic field. The situation with no electromagnetic field requires a negative matter pressure (tension) on the boundary. On the other hand, the situation with an electromagnetic field demands zero matter pressure on the boundary. So in this situation an electrified quasiblack hole can be obtained by the gradual compactification of a relativistic star with the usual zero pressure boundary condition. For the nonextremal case inside the density necessarily acquires a jump on the boundary, a fact with no harmful consequences whatsoever, whereas for the extremal case the density is continuous at the boundary. For the extremal case inside we also state and prove the proposition that such a quasiblack hole cannot be made from phantom matter at the quasihorizon. The regularity condition for the extremal case, but not for the nonextremal one, can be obtained from the known regularity condition for usual black holes.

In this paper we present trispectrum estimation methods which can be applied to general nonseparable primordial and CMB trispectra. We review the relationship between the reduced CMB trispectrum and the reduced primordial trispectrum. We present a general optimal estimator for the connected part of the trispectrum, for which we derive a quadratic term to incorporate the effects of inhomogeneous noise and masking. We describe a general algorithm for creating simulated maps with given arbitrary (and independent) power spectra, bispectra, and trispectra. We propose a universal definition of the trispectrum parameter $T_{NL}$, so that the integrated trispectrum on the observational domain can be consistently compared between theoretical models. We define a shape function for the primordial trispectrum, together with a shape correlator and a useful parametrization for visualizing the trispectrum; these methods might also be applied to the late-time trispectrum for large-scale structure. We derive separable analytic CMB solutions in the large-angle limit for constant and local models. We present separable mode decompositions which can be used to describe any primordial or CMB trispectra on their respective wave number or multipole domains. By extracting coefficients of these separable basis functions from an observational map, we are able to present an efficient estimator for any given theoretical model with a nonseparable trispectrum. The estimator has two manifestations, comparing the theoretical and observed coefficients at either primordial or late times, thus encompassing a wider range of models, such as secondary anisotropies, lensing, and cosmic strings. We show that these mode decomposition methods are numerically tractable with order $l^5$ operations for the CMB estimator and approximately order $l^6$ for the general primordial estimator (reducing to order $l^3$ in both cases for a special class of models). We also demonstrate how the trispectrum can be reconstructed from observational maps using these methods.

Observations of the frequency dependence of the global brightness temperature of the redshifted 21 cm line of neutral hydrogen may be possible with single dipole experiments. In this paper, we develop a Fisher matrix formalism for calculating the sensitivity of such instruments to the 21 cm signal from reionization and the dark ages. We show that rapid reionization histories with duration $\Delta z\lesssim 2$ can be constrained, provided that local foregrounds can be well modeled by low order polynomials. It is then shown that observations in the range $\nu =50–100\mathrm{MHz}$ can feasibly constrain the $\mathrm{Ly}\alpha$ and x-ray emissivity of the first stars forming at $z\sim 15–25$, provided that systematic temperature residuals can be controlled to less than 1 mK. Finally, we demonstrate the difficulty of detecting the 21 cm signal from the dark ages before star formation.

The standard model of particle theory will be rigorously tested by upcoming precision data on flavor mixing. Although the unitarity triangles ($UTs$) carry information about the Kobayashi-Maskawa (KM) quark mixing matrix, it explicitly contains just three parameters which is one short to completely fix the KM matrix. We have recently shown that the unitarity boomerangs ($UBs$) formed using two $UTs$, with a common inner angle, can completely determine the KM matrix and, therefore, better represents quark mixing. Out of the total 18 possible $UBs$, there is only one that does not involve very small angles and is the ideal one for practical uses. Although the $UBs$ have different areas, there is, however, an invariant quantity, for all $UBs$, which is equal to a quarter of the Jarlskog parameter $J$ squared. Hunting for new physics, with a unitarity boomerang, can reveal more information, than just using a $UTs$.

We consider the three-body decays of gravitino dark matter in supersymmetric scenarios with bilinear $R$-parity violation. In particular, gravitino decays into $\ell W^{*}$ ($\ell f{\overline{f}}^{\prime }$) and $\nu Z^{*}$ ($\nu f\overline{f}$) are examined for gravitino masses below $M_W$. After computing the gravitino decay rates into these three-body final states and studying their dependence on supersymmetric parameters, we find that these new decay modes are often more important than the two-body decay, into a photon and a neutrino, considered in previous works. Consequently, the gravitino lifetime and its branching ratios are substantially modified, with important implications for the indirect detection of gravitino dark matter.