We investigate theoretical and observational aspects of a time-dependent parameterization for the dark energy equation of state $w\left(z\right)$, which is a well behaved function of the redshift $z$ over the entire cosmological evolution, i.e., $z\in [-1,\infty )$. By using a theoretical algorithm of constructing the quintessence potential directly from the $w\left(z\right)$ function, we derive and discuss the general features of the resulting potential for the cases in which dark energy is separately conserved and when it is coupled to dark matter. Since the parameterization here discussed allows us to divide the parametric plane in defined regions associated to distinct classes of dark energy models, we use some of the most recent observations from type Ia supernovae, baryon acoustic oscillation peak and Cosmic Microwave Background shift parameter to check which class is observationally preferred. We show that the largest portion of the confidence contours lies into the region corresponding to a possible crossing of the so-called phantom divide line at some point of the cosmic evolution.

Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term $\chi$. The hypersurface of discontinuity propagates at finite velocity determined by finite increment $\Delta \chi ={\chi }_{+}-{\chi }_{-}$. The current increases ${\chi }_{+}>{\chi }_{-}$ in stable shocks, but transition between spacelike ($\chi >0$) and timelike ($\chi <0$) currents is impossible.

We systematically study the spectrum of excitations and the one-loop determinant of holographic Wilson loop operators in antisymmetric representations of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Holographically, these operators are described by D5-branes carrying electric flux and wrapping an $S^4\subset S^5$ in the ${\mathrm{AdS}}_5\times S^5$ bulk background. We derive the dynamics of both bosonic and fermionic excitations for such D5-branes. A particularly important configuration in this class is the D5-brane with ${\mathrm{AdS}}_2\times S^4$ world volume and $k$ units of electric flux, which is dual to the circular Wilson loop in the totally antisymmetric representation of rank $k$. For this Wilson loop, we obtain the spectrum, show explicitly that it is supersymmetric and calculate the one-loop effective action using heat kernel techniques.

We discuss the prospects for improved upper limits on neutrino masses that may be provided by a core-collapse supernova explosion in our Galaxy, if it exhibits time variations in the neutrino emissions on the scale of a few milliseconds as suggested by recent two-dimensional simulations. Analyzing simulations of such neutrino emissions using the wavelet technique adopted in [J. Ellis, H.-T. Janka, N. E. Mavromatos, A. S. Sakharov, and E. K. G. Sarkisyan, Phys. Rev. D 85, 045032 (2012)], we find that an upper limit $m_{\nu }\sim 0.14\mathrm{eV}$ could be established at the 95% confidence level if the time variations in emissions were to be preserved during neutrino propagation to the Earth.

We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semiclassical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory on ${\mathbf{R}}^2\times {\mathbf{S}}_L^1\times {\mathbf{S}}_{\beta }^1$. At large $N$, fixed-$L$, and arbitrary $\beta$, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large $N$ expansion. At fixed-$N$, small $L$ and a range of $\beta$, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak [J. Liao and E. Shuryak, Phys. Rev. C 75, 054907 (2007).] regarding the magnetic component of the quark-gluon plasma at RHIC.

We numerically investigate the solutions to the effective equations of the Bianchi II model within the “improved” loop quantum cosmology dynamics. The matter source is a massless scalar field. We perform a systematic study of the space of solutions, and focus on the behavior of several geometrical observables. We show that the big bang singularity is replaced by a bounce and the pointlike singularities do not saturate the energy density bound. There are up to three directional bounces in the scale factors, one global bounce in the expansion, the shear presents up to four local maxima and can be zero at the bounce. This allows for solutions with density larger than the maximal density for the isotropic and Bianchi I cases. The asymptotic behavior is shown to behave like that of a Bianchi I model, and the effective solutions connect anisotropic solutions even when the shear is zero at the bounce. All known facts of Bianchi I are reproduced. In the “vacuum limit,” solutions are such that almost all the dynamics is due to the anisotropies. Since Bianchi II plays an important role in the Bianchi IX model and the Belinskii, Khalatnikov, Lifshitz conjecture, our results can provide an intuitive understanding of the behavior in the vicinity of general spacelike singularities, when loop-geometric corrections are present.

The stochastic gravitational wave background (GWB) from halo mergers is investigated by a quasianalytic method. The method we employ consists of two steps. The first step is to construct a merger tree by using the extended Press-Schechter formalism or the Sheth & Tormen formalism, with Monte Carlo realizations. This merger tree provides evolution of halo masses. From $N$-body simulation of two-halo mergers, we can estimate the amount of gravitational wave emission induced by the individual merger process. Therefore, the second step is to combine this gravitational wave emission with the merger tree and obtain the amplitude of the GWB. We find ${\Omega }_{\mathrm{GW}}\sim {10}^{-19}$ for $f\sim {10}^{-17}–{10}^{-16}\mathrm{Hz}$, where ${\Omega }_{\mathrm{GW}}$ is the energy density of the GWB. It turns out that most of the contribution on the GWB comes from halos with masses below ${10}^{15}{M}_{\odot }$ and mergers at low redshift, i.e., $0<z<0.8$.

We obtain traversable wormhole and time machine solutions of the field equations of an alternative of gravity with nonminimally curvature-matter coupling. Our solutions exhibit a nontrivial redshift function and allow for matter that satisfies the dominant energy condition.

The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be rapidly changing with time, and shows that entropy increases when comparing any slice of the horizon to any earlier slice. The proof requires the existence of an algebra of observables restricted to the horizon, satisfying certain axioms (determinism, ultralocality, local Lorentz invariance, and stability). These axioms are explicitly verified in the case of free fields of various spins, as well as $1+1$ conformal field theories. The validity of the axioms for other interacting theories is discussed.

We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. The solution has a curvature singularity located at the origin, where also the scalar field diverges. Since there is no event horizon surrounding this singularity, the solution describes a naked singularity dressed with a nontrivial scalar field. This spacetime is an asymptotically locally anti–de Sitter one when the Ricci-flat base manifold is locally flat. The asymptotic solution for an arbitrary Einstein base manifold is found and the corresponding mass, calculated through the canonical generator of the time-translation invariance, is shown to be finite. The contribution to the mass from the scalar field at infinity is also discussed.

We show that a conformal-invariance–violating coupling of the inflaton to electromagnetism produces a cross correlation between curvature fluctuations and a spectrum of primordial magnetic fields. According to this model, in the case of power-law inflation, a primordial magnetic field is generated with a nearly flat power spectrum and rms amplitude ranging from nG to pG. We study the cross correlation, a three-point function of the curvature perturbation, and two powers of the magnetic field, in real and momentum space. The cross-correlation coefficient, a dimensionless ratio of the three-point function with the curvature-perturbation and magnetic-field power spectra, can be several orders of magnitude larger than expected as based on the amplitude of scalar metric perturbations from inflation. In momentum space, the cross-correlation peaks for flattened triangle configurations, and is 3 orders of magnitude larger than the squeezed triangle configuration. These results suggest likely methods for distinguishing the observational signatures of the model.

Features in the inflaton potential that are traversed in much less than an $e$-fold of the expansion can produce observably large non-Gaussianity. In these models first-order corrections to the curvature mode function evolution induce effects at second order in the slow-roll parameters that are generically greater than $\sim 10\%$ and can reach order unity for order unity power spectrum features. From a complete first-order expression in generalized slow roll, we devise a computationally efficient method that is as simple to evaluate as the leading-order one and implements consistency relations in a controlled fashion. This expression matches direct numerical computation for step potential models of the dominant bispectrum configurations to better than 1% when features are small and 10% when features are order unity.

We study the photon self-energy for the in-medium photon in a three-flavor color superconductor in the presence of a magnetic field. At strong magnetic field, the quark dynamics becomes $(1+1)$-dimensional and the self-energy tensor only has longitudinal components. In this approximation there is no Debye or Meissner screenings at zero temperature, but the electric susceptibility is nonzero and highly anisotropic. In the direction transverse to the applied field, the electric susceptibility is the same as in vacuum, while in the longitudinal direction it depends on the magnitude of the magnetic field. Such a behavior is a realization in cold-dense QCD of the magnetoelectric effect, which was first discovered in condensed matter physics. The magnetic permeability remains equal to that in vacuum for both transverse and longitudinal components. We discuss the importance of the Pauli-Villars regularization to get meaningful physical results in the infrared limit of the polarization operator. We also find the covariant form of the polarization operator in the reduced $(1+1)$-D space of the lowest Landau level and prove its transversality.

We analytically study the evolution of gravitational instability of self-gravitating dark matter within the framework of a nonrelativistic “hydrodynamical” model of the Universe, valid for scales that are small compared to the Hubble scale and for distances far away from black holes. We propose a particular form for parametrization of the particle distribution function via macroscopic quantities, such that the initial dispersion of microscopic velocities is not neglected, but plays a determinant role. Thus our model may be called a modified cold dark matter model. We found an analytical solution which indicates that a spontaneous spatially localized fluctuation of velocity generates density perturbations relative to initially unperturbed background. For the instability to arise, we do not need to assume any initial density (metric) fluctuations. The evolving perturbation is hydrodynamically unstable in the self-gravitating expanding Universe and can produce both—regions where no dark matter accumulates and halolike regions where dark matter does accumulate. The perturbation region boundary propagates as a shock wave with a speed that is time varying, until eventually reaching its steady state. We also derive an explicit analytical expression for the correlation function $R({\mathbf{x}}_1-{\mathbf{x}}_2)$ of density fluctuations, which can be compared by experimentalists with data from astrophysical observations.

We investigate the expected neutrino emissivity from nuclear collisions in a magnetically dominated model of gamma-ray bursts motivated by recent observational and theoretical developments. The results indicate that small multi-GeV neutrino fluxes are expected for model parameter values which are typical of electromagnetically detected bursts. We show that for detecting at least one muon event in IceCube and its DeepCore subarray, a single burst must be near the high end of the luminosity function, and at low redshifts $z\lesssim 0.1$, where the burst rate is very low. We also calculate the luminosity and distance ranges which can generate 0.01–1 muon events per gamma-ray burst in the same detectors, which may be of interest if simultaneously detected electromagnetically, or if measured with future extensions of IceCube or other neutrino detectors with larger effective volume and better sensitivity.

We investigate the critical dynamics of $O(N)$-symmetric scalar field theories to determine the critical exponents of transport coefficients as a second-order phase transition is approached from the symmetric phase. A set of stochastic equations of motion for the slow modes is formulated, and the long-wavelength dynamics is examined for an arbitrary number of field components $N$ in the framework of the dynamical renormalization group within the $\epsilon$ expansion. We find that for a single component scalar field theory, $N=1$, the system reduces to the model C of critical dynamics, whereas for $N>1$, the model G is effectively restored owing to dominance of $O(N)$-symmetric charge fluctuations. In both cases, the shear viscosity remains finite in the critical region. On the other hand, we find that the bulk viscosity diverges as the correlation length squared, for $N=1$, while it remains finite for $N>1$.

Within a spontaneously broken gauge group we carefully analyze and calculate triple gauge boson vertices dominated by triangle one-loop Feynman diagrams involving heavy fermions compared to external momenta and gauge boson masses. We perform our calculation strictly in four dimensions and derive a general formula for the off-shell, one-particle irreducible (1PI) effective vertex which satisfies the relevant Ward Identities and the Goldstone boson equivalence theorem. Our goal is to search for nondecoupling heavy fermion effects highlighting their synergy with gauge chiral anomalies. Particularly in the standard model, we find that when the arbitrary anomaly parameters are fixed by gauge invariance and/or Bose symmetry, the heavy fermion contribution cancels its anomaly contribution leaving behind anomaly and mass independent contributions from the light fermions. We apply these results in calculating the corresponding $CP$-invariant one-loop induced corrections to triple gauge boson vertices in the SM, minimal $Z^{\prime }$ models as well as their extensions with a fourth fermion generation, and compare with experimental data.

It is challenging for supersymmetry if the 125 GeV Higgs boson is confirmed by the LHC. In the case of small squark mixing it is inevitable to introduce heavy top squarks to lift the Higgs mass that is hard to be produced by the LHC. Here we consider the possibility that in gauge mediation the superparticles belonging to $SU(2)$ doublets are much heavier than those do not carry the $SU(2)$ quantum numbers. Under the assumption not only the Higgs mass can be large enough but also there are light right-handed top squarks below the TeV scale that can be observed in future.

We study the phase diagram of a chiral random matrix model with three quark flavors at finite temperature and chemical potential, taking the chiral and diquark condensates as independent order parameters. Fixing the ratio of the coupling strengths in the quark-antiquark and quark-quark channels applying the Fierz transformation, we find that the color-flavor locked (CFL) phase is realized at large chemical potential, while the ordinary chirally broken phase appears in the region with small chemical potential. We investigate responses of the phases by changing small quark masses in the cases with three equal-mass flavors and with $2+1$ flavors. In the case with three equal-mass flavors, we find that the finite masses make the CFL phase transition line move to the higher-density region. In the case with $2+1$ flavors, we find the two-flavor color-superconducting phase at the medium-density region as a result of the finite asymmetry between the flavors, as well as the CFL phase at the higher-density region.

A chiral field theory of mesons has been applied to study the contribution of the current quark masses to the ${\pi }^0\to \gamma \gamma$ decay width at the next leading order. In this study, the large $N_C$ limit is assumed in order that the approach performed is consistent. The consequence that some low-energy constants from $\mathcal{L}(6{)}_{\mathrm{WZW}}$ can be read off from the final expressions is an interesting result. $(1.44\pm 0.67)\%$ enhancement has been predicted and there is no new parameter.