The zeta function regularization technique is used to study the finite temperature Casimir effect for a charged and massless scalar field confined between parallel plates and satisfying Dirichlet boundary conditions at the plates. A magnetic field perpendicular to the plates is included. Three equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature and plate distance. These expressions of the zeta function are used to calculate the Helmholtz free energy of the scalar field and the pressure on the plates, in the case of high temperature, small plate distance and strong magnetic field. In all cases, simple analytic expressions are obtained for the free energy and pressure which are accurate and valid for practically all values of temperature, plate distance and magnetic field.

We study, in the framework of open quantum systems, the entanglement generation between two mutually independent static two-level atoms in de Sitter spacetime. We treat the two-atom system as an open system in interaction with a bath of fluctuating conformally coupled massless scalar fields in the de Sitter invariant vacuum and derive the master equation that governs its evolution. With the help of the partial transposition criterion, we analyze entanglement generation between the two initially separable atoms and find that static atoms in de Sitter spacetime exhibit distinct characteristics from those in a thermal bath in flat spacetime in terms of entanglement generation. So, in principle, one can tell whether he is in a thermal bath or in de Sitter space by checking the entanglement creation between two initially separable static atoms in certain circumstances.

The AMS-02 experiment has recently released data which confirms a rise in the cosmic-ray positron fraction as a function of energy up to approximately 350 GeV. Over the past decade, attempts to interpret this positron excess in terms of dark-matter decays have become increasingly complex and have led to a number of general expectations about the decaying dark-matter particles: such particles cannot undergo simple two-body decays to leptons, for example, and they must have rather heavy TeV-scale masses. In this paper, by contrast, we show that Dynamical Dark Matter can not only match existing AMS-02 data on the positron excess, but also accomplish this feat with significantly lighter dark-matter constituents undergoing simple two-body decays to leptons. Moreover, we demonstrate that this can be done without running afoul of numerous other competing constraints from FERMI and Planck on decaying dark matter. Finally, we demonstrate that the Dynamical Dark Matter framework makes a fairly robust prediction that the positron fraction should level off and then remain roughly constant out to approximately 1 TeV, without experiencing any sharp downturns. Indeed, if we interpret the positron excess in terms of decaying dark matter, we find that the existence of a plateau in the positron fraction at energies less than 1 TeV may be taken as a “smoking gun” of Dynamical Dark Matter.

In this paper, we study the nonlinear matter power spectrum in a specific family of $f(R)$ models that can reproduce the $\Lambda \mathrm{CDM}$ background expansion history, using high resolution $N$-body simulations based on the ecosmog code. We measure the matter power spectrum in the range of $0.05h{\mathrm{Mpc}}^{-1}<k<10h{\mathrm{Mpc}}^{-1}$ from simulations for our $f(R)$ models and give theoretical explanations to their behavior and evolution patterns. We also examine the chameleon mechanism for our models and find that it works throughout the cosmic history in dense regions, for our $f(R)$ models with $|f_{R0}|<{10}^{-4}$. On the other hand, for models with $|f_{R0}|>{10}^{-3}$, we find no chameleon screening in dense regions at late times ($z<3$), which means that those models could be ruled out due to the factor-of-$1/3$ enhancement to the strength of Newtonian gravity. We also give the best-fit parameters for a generalized parametrized post-Friedman fitting formula, which works well for the models studied here.

We describe a general procedure for using number counts of any object to constrain the probability distribution of the primordial fluctuations, allowing for generic weak non-Gaussianity. We apply this procedure to use limits on the abundance of primordial black holes and dark matter ultracompact minihalos to characterize the allowed statistics of primordial fluctuations on very small scales. We present constraints on the power spectrum and the amplitude of the skewness for two different families of non-Gaussian distributions, distinguished by the relative importance of higher moments. Although primordial black holes probe the smallest scales, ultracompact minihalos provide significantly stronger constraints on the power spectrum and so are more likely to eventually provide small-scale constraints on non-Gaussianity.

Gravitational-wave diagnostics are developed for discriminating between varieties of mixed poloidal-toroidal magnetic fields in neutron stars, with particular emphasis on differentially rotating protoneutron stars. It is shown that tilted torus magnetic fields, defined as the sum of an internal/external poloidal component, whose axis of symmetry is tilted with respect to the rotation axis, and an internal toroidal component, whose axis of symmetry is aligned with the rotation axis, deform the star triaxially, unlike twisted torus fields, which deform the star biaxially. Utilizing an analytic tilted torus example, we show that these two topologies can be distinguished by their gravitational wave spectrum and polarization phase portraits. For example, the relative amplitudes and frequencies of the spectral peaks allow one to infer the relative strengths of the toroidal and poloidal components of the field, and the magnetic inclination angle. Finally, we show how a tilted torus field arises naturally from magnetohydrodynamic simulations of differentially rotating neutron stars, and how the gravitational wave spectrum evolves as the internal toroidal field winds up. These results point to the sorts of experiments that may become possible once gravitational wave interferometers detect core-collapse supernovae routinely.

$S_3$ models offer a low energy approach to describe the observed pattern of masses and mixing, of both quarks and leptons. In this work, we first revisit an $S_3$ model with only one Higgs electroweak doublet, where the flavor symmetry must be broken in order to produce an acceptable pattern of masses and mixing for fermions. Then, we analyze different $S_3$ models where the flavor symmetry is preserved as an exact but hidden symmetry of the low energy spectra after the electroweak symmetry breaking. The latter models require the addition of two more Higgs electroweak doublets which are accommodated in an $S_3$ doublet. We also explore the consequences of adding a fourth Higgs electroweak doublet, thus occupying all three irreducible representations of $S_3$. We show how the various $S_3$-invariant mass matrices of the different models can reproduce the two texture zeros and nearest neighbor interaction matrix forms, which have been found to provide a viable and universal treatment of mixing for both quarks and leptons. We also find analytical and exact expressions for the Cabibbo-Kobayashi-Maskawa (CKM) matrix of the models in terms of quark mass ratios. Finally, we compare the expressions of the CKM matrix of the different $S_3$ models with the most up to date values of masses and mixing in the quark sector, via a ${\chi }^2$ analysis. We find that the analytical expressions we derived reproduce remarkably well the most recent experimental data of the CKM matrix, suggesting that $S_3$ is a symmetry of the quark sector.

Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation for the fermion self-energy, i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap-equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed fermion–gauge boson vertex is an important factor in deciding the issue.

The “gravitational baryogenesis” scenario is extended to generate both baryon and dark matter asymmetries in the matter dominated era corresponding to post-inflationary reheating. A minimal extension requires a singlet fermion $X$ for dark matter and a singlet scalar $S$. With two or more hidden sector fermions, the scenario can lead to nucleon decay into dark matter with a lifetime of order ${10}^{34–36}\mathrm{yr}$, which is relevant for current or future experiments. The correct multicomponent relic density can be obtained if dark matter fermions couple to a sub-GeV vector boson that weakly interacts with the standard model through mixing. The typical inflationary scale in the scenario is of order ${10}^{16}\mathrm{GeV}$ which suggests that tensor mode perturbations could potentially be within observational reach.

We present a measurement of the muon charge asymmetry from the decay of the $W$ boson via $W\to \mu \nu$ using $7.3{\mathrm{fb}}^{-1}$ of integrated luminosity collected with the D0 detector at the Fermilab Tevatron Collider at $\sqrt{s}=1.96\mathrm{TeV}$. The muon charge asymmetry is presented in two kinematic regions in muon transverse momentum and event missing transverse energy: ($p_T^{\mu }>25\mathrm{GeV}$, ${\mathrm{E̸}}_T>25\mathrm{GeV}$) and ($p_T^{\mu }>35\mathrm{GeV}$, ${\mathrm{E̸}}_T>35\mathrm{GeV}$). The measured asymmetries are compared with theory predictions made using three parton distribution function sets. The data at $p_T^{\mu }>35\mathrm{GeV}$, ${\mathrm{E̸}}_T>35\mathrm{GeV}$, and larger values of $|{\eta }^{\mu }|$ favor an increased $d(x)/u(x)$ ratio at higher values of $x$ than is predicted.

We give a holographic explanation of how the renormalization group approach to singular perturbations in nonlinear differential equations proposed by Chen, Goldenfeld, and Oono is indeed equivalent to a renormalization group method in quantum field theories proposed by Gell-Mann and Low via AdS/CFT correspondence.

The Cauchy formalism of numerical relativity has been successfully applied to simulate various dynamical spacetimes without any symmetry assumption. But discovering how to set a mathematically consistent and physically realistic boundary condition is still an open problem for Cauchy formalism. In addition, the numerical truncation error and finite region ambiguity affect the accuracy of gravitational wave form calculation. As to the finite region ambiguity issue, the characteristic extraction method helps much. But it does not solve all of the above issues. Besides the above problems for Cauchy formalism, the computational efficiency is another problem. Although characteristic formalism of numerical relativity suffers the difficulty from caustics in the inner near zone, it has advantages in relation to all of the issues listed above. Cauchy-characteristic matching (CCM) is a possible way to take advantage of characteristic formalism regarding these issues and treat the inner caustics at the same time. CCM has difficulty treating the gauge difference between the Cauchy part and the characteristic part. We propose generalized Bondi-Sachs equations for characteristic formalism for the Cauchy-characteristic matching end. Our proposal gives out a possible same numerical evolution scheme for both the Cauchy part and the characteristic part. And our generalized Bondi-Sachs equations have one adjustable gauge freedom which can be used to relate the gauge used in the Cauchy part. Then these equations can make the Cauchy part and the characteristic part share a consistent gauge condition. So our proposal gives a possible new starting point for Cauchy-characteristic matching.

The late stages of large-scale structure evolution are treated semianalytically within the framework of the modified halo model. We suggest a simple yet accurate approximation for relating the nonlinear amplitude to the linear one for spherical density perturbation. For halo concentration parameter $c$, a new computation technique is proposed, which eliminates the need for interim evaluation of the $z_{\mathrm{col}}$. The validity of the technique is proved for $\Lambda \mathrm{CDM}$ and $\Lambda \mathrm{WDM}$ cosmologies. Also, the parameters for the Sheth-Tormen mass function are estimated. The modified and extended halo model is applied for determination of the nonlinear power spectrum of dark matter, as well as for a galaxy power spectrum estimation. The semianalytical techniques for the dark matter power spectrum are verified by comparison with data from numerical simulations. Also, the predictions for the galaxy power spectra are confronted with ’’observed’’ data from the Infrared Astronomical Satellite Point Source Catalog Redshift Survey (PSCz) and Sloan Digital Sky Survey (SDSS) galaxy catalogs, good accordance is found.

We perform a semiclassical analysis of the emergent universe scenario for inflation. Fixing the background, and taking the inflaton to be homogenous, we cast the inflaton’s evolution as a one-dimensional quantum mechanics problem. The potential is taken to be flat or linear, as an approximation to the monotonic and slowly varying asymptotic behavior of the emergent universe potential. We find that the tuning required over a long time scale for this inflationary scenario is unstable quantum mechanically. Considering the inflaton field value as a wave packet, the spreading of the wave packet destroys any chance of both starting and ending with a well-formed state. Thus, one cannot have an Einstein static universe to begin with that evolves into a well-defined beginning to inflation a long time later.

A phenomenological model of dark energy that tracks the baryonic and cold dark matter at early times but resembles a cosmological constant at late times is explored. In the transition between these two regimes, the dark energy density drops rapidly as if it were a relic species that freezes out, during which time the equation of state peaks at $+1$. Such an adjustment in the dark energy density, as it shifts from scaling to potential domination, could be the signature of a trigger mechanism that helps explain the late-time cosmic acceleration. We show that the non-negligible dark energy density at early times, and the subsequent peak in the equation of state at the transition, leave an imprint on the cosmic microwave background anisotropy pattern and the rate of growth of large scale structure. The model introduces two new parameters, consisting of the present-day equation of state and the redshift of the freeze-out transition. A Monte Carlo Markov chain analysis of a ten-dimensional parameter space is performed to compare the model with pre-Planck cosmic microwave background, large scale structure and supernova data and measurements of the Hubble constant. We find that the transition described by this model could have taken place as late as a redshift $z\sim 250$. We explore the capability of future cosmic microwave background and weak lensing experiments to put tighter constraints on this model. The viability of this model may suggest new directions in dark-energy model building that address the coincidence problem.

Long duration gamma-ray bursts are powerful sources that can accelerate particles to ultrahigh energies. Acceleration of protons in the forward shock of the highly relativistic gamma-ray burst (GRB) blastwave allows PeV-EeV neutrino production by photopion interactions of ultrahigh energy protons with x-ray to optical photons of the GRB afterglow emission. Four different blastwave evolution scenarios are considered: adiabatic and fully radiative blastwaves in a constant density circumburst medium and in a wind environment with the particle density in the wind decreasing inversely proportional to the square of the radius from the center of the burst. The duration of the neutrino flux depends on the evolution of the blastwave and can last up to a day in the case of an adiabatic blastwave in a constant density medium. Neutrino fluxes from the three other blastwave evolution scenarios are also calculated. Diffuse neutrino fluxes calculated using the observed rate of long-duration GRBs are consistent with the recent IceCube upper limit on the prompt GRB neutrino flux below PeV. The diffuse neutrino flux needed to explain the two neutrino events at PeV energies recently detected by IceCube can partially come from the presented GRB blastwave diffuse fluxes. Future observations by IceCube and upcoming huge radio Askaryan experiments will be able to probe the flux models presented here or constrain the GRB blastwave properties.

We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The idea can be easily adapted to other branches of physics and computational science that employ Monte Carlo methods. The error reduction techniques, referred to as covariant approximation averaging, utilize approximations which are covariant under lattice symmetry transformations. We observe cost reductions from the new method compared to the traditional one, for fixed statistical error, of 16 times for the nucleon mass at $M_{\pi }\sim 330\mathrm{MeV}$ (domain-wall quark) and 2.6–20 times for the hadronic vacuum polarization at $M_{\pi }\sim 315\mathrm{MeV}$ (Asqtad quark). These cost reductions should improve with decreasing quark mass and increasing lattice sizes.

Random matrix theory has been successfully applied to lattice quantum chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson-Dirac operator. In this paper, we study the infrared spectrum of the Wilson-Dirac operator via random matrix theory including the three leading order $a^2$ correction terms that appear in the corresponding chiral Lagrangian. A derivation of the joint probability density of the eigenvalues is presented. This result is used to calculate the density of the complex eigenvalues, the density of the real eigenvalues, and the distribution of the chiralities over the real eigenvalues. A detailed discussion of these quantities shows how each low-energy constant affects the spectrum. Especially we consider the limit of small and large (which is almost the mean field limit) lattice spacing. Comparisons with Monte Carlo simulations of the random matrix theory show a perfect agreement with the analytical predictions. Furthermore we present some quantities which can be easily used for comparison of lattice data and the analytical results.

Using the field-theory-inspired expression for the pion electromagnetic form factor $F_{\pi }$, a good description of the data in the range $-10<s<1{\mathrm{GeV}}^2$ is obtained upon taking into account the pseudoscalar-pseudoscalar (PP) loops. When the vector-pseudoscalar (VP) and the axial vector–pseudoscalar (AP) loops are taken into account in addition to the PP ones, a good description of the BABAR data on the reaction $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ is obtained at energies up to 3 GeV. The inclusion of the VP and AP loops demands the treatment of the reactions $e^{+}{e}^{-}\to \omega {\pi }^0$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$. This task is performed with the SND data on $\omega {\pi }^0$ production and the BABAR data on ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ production, both in $e^{+}{e}^{-}$ annihilation, by taking into account $\rho (770)$ and the heavier $\rho (1450)$, $\rho (1700)$, and $\rho (2100)$ resonances. The problems arising from including the VP and AP loops are pointed out and discussed.

It is known that the spherically symmetric singular Wu-Yang monopole solution of the SU(2) gauge field equations is equivalent to the Dirac U(1) monopole (with one gauge group embedded into the other). We consider a multicenter configuration of $k$ Dirac monopoles and its embedding into SU(3) gauge theory. Using this embedding, we construct an explicit multimonopole solution of the SU(3) Yang-Mills equations which generalizes the SU(2) Wu-Yang solution and the known spherically symmetric point SU(3) monopole solutions.