For the past decade, gravitational lensing in the strong gravitational field has been studied eagerly. It is well known that, for the lensing by a black hole, an infinite number of Einstein rings are formed by the light rays which wind around the black hole nearly on the photon sphere, which are called relativistic Einstein rings. This is also the case for the lensing by a wormhole. In this paper, we study the Einstein ring and relativistic Einstein rings for the Schwarzschild black hole and the Ellis wormhole, the latter of which is an example of traversable wormholes of the Morris-Thorne class. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. We conclude that we can detect the relativistic Einstein rings by wormholes which have the radii of the throat $a\simeq 0.5\mathrm{pc}$ at a Galactic center with the distance 10 Mpc and which have $a\simeq 10\mathrm{AU}$ in our Galaxy using the most powerful modern instruments which have the resolution of ${10}^{-2}\mathrm{arcsecond}$ such as a 10-meter optical-infrared telescope. The black holes which make the Einstein rings of the same size as the ones by the wormholes are galactic supermassive black holes and the relativistic Einstein rings by the black holes are too small to measure with the current technology. We may test the hypotheses of astrophysical wormholes by using the Einstein ring and relativistic Einstein rings in the future.

We prove the existence of general relativistic perfect fluid black hole solutions, and demonstrate the phenomenon for the $P=w\rho$ class of equations of state. While admitting a local timelike Killing vector on the event horizon itself, the various black hole configurations are necessarily time dependent (thereby avoiding a well known no-go theorem) away from the horizon. Consistently, Hawking’s imaginary time periodicity is globally manifest on the entire spacetime manifold.

Rainbow, glory and orbiting scattering are usually described by the properties of the classical deflection function related to the real part of the quantum mechanical scattering phase shift or by the diffractive pattern of the quantum mechanical cross sections. Here we show that the case of orbiting scattering of massless spin 0, 1 and 2 particles from Schwarzschild black holes can be characterized by a sudden rise in $|R_l{|}^2$ at a critical angular momentum $l_C$, which we show corresponds to the unstable circular orbits of these particles. For the cases $s=0$, 2, we attempt a new interpretation of the Regge-Wheeler potential by identifying the quantum mechanical corrections to the effective potential of massless particles. We probe into the black hole scattering by using numerical and semi-analytical methods which give very good agreements with the exact numerical results. The limitations of previously used approximations as compared to the exact and semi-analytical results are discussed.

We investigate the cosmological reconstruction in an anisotropic universe for both the homogeneous and inhomogeneous content of the universe. Special attention is given to three interesting cases: Bianchi type I, Bianchi type III, and Kantowski-Sachs models. The de Sitter, power-law, and general exponential solutions are assumed for the scale factor in each spatial direction and the corresponding cosmological models are reconstructed. Moreover, for the general exponential solutions—from which the de Sitter and power-law solutions may be obtained—we obtain models which reproduce the early Universe (assuming inflation) and the late-time accelerated expanding Universe. The models obtained for the late-time Universe are consistent with a known result in the literature where a power-law type correction in $T$ is added to a power-law type of $f(T)$ for guaranteeing the avoidance of the big rip and the big freeze.

We study the cosmological perturbations for the possible inflation scenario in the teleparallel equivalence of general relativity specified with parallelizable topological conditions. By acquiring the identical physical observables to general relativity under the teleparallel formalism, we perform a $3+1$ decomposition of the vierbein field, which can be interpreted as the time-gauge fixing between coordinate and tangent frames. We also extend our discussion to the higher-order action, $f(T)$ gravity.

We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for determining free data based on superposition, as well as a way to handle black hole singularities without excision. We numerically solve the constraint equations using a multigrid algorithm with mesh refinement. We demonstrate the efficacy of the method with initial data solutions for several applications: a quasicircular binary black hole merger, a dynamical capture black hole-neutron star merger, and an ultrarelativistic collision.

We argue that if the UV cutoff of an effective field theory with many low energy degrees of freedom is of the order, or below, the scale of the stretched horizon in a black hole background, which in turn is significantly lower than the Planck scale, the black hole radiance rate may not be enhanced by the emission of all the light IR modes. Instead, there may be additional suppressions hidden in the UV completion of the field theory, which really control which light modes can be emitted by the black hole. It could turn out that many degrees of freedom cannot be efficiently emitted by the black hole, and so the radiance rate may be much smaller than its estimate based on the counting of the light IR degrees of freedom. If we apply this argument to the Randall-Sundrum II (RS2) brane world, it implies that the emission rates of the low energy conformal field theory modes will be dramatically suppressed: its UV completion is given by the bulk gravity on ${\mathrm{AdS}}_5\times S^5$, and the only bulk modes which could be emitted by a black hole are the 4-dimensional (4D) $s$ waves of bulk modes with small 5-dimensional momentum, or equivalently, small 4D masses. Further, their emission is suppressed by bulk warping, which lowers the radiation rate much below the IR estimate, yielding a radiation flux $\sim (T_{\mathrm{BH}}L{)}^2{\mathcal{L}}_{\mathrm{Hawking}}\sim (T_{\mathrm{BH}}/M_{\mathrm{Pl}}{)}^{2}N{\mathcal{L}}_{\mathrm{Hawking}}$, where ${\mathcal{L}}_{\mathrm{Hawking}}$ is the Hawking radiation rate of a single light species. This follows directly from low conformal field theory cutoff $\mu \sim L^{-1}\ll M_{\mathrm{Pl}}$, a large number of modes $N\gg 1$ and the fact that 4D gravity in RS2 is induced, $M_{\mathrm{Pl}}^2\simeq N{\mu }^2$.

We calculate the antideuteron yield in dark matter annihilations on an event-by-event basis using the herwig$++$ Monte Carlo generator. We present the resulting antideuteron fluxes for quark and gauge boson final states. As deuteron production in the coalescence model depends on momentum differences between nucleons that are small compared to ${\Lambda }_{\mathrm{QCD}}$, it is potentially very sensitive to the hadronization model employed. We therefore compare our antideuteron yields to earlier results based on pythia, thereby estimating their uncertainties. We also briefly discuss the importance of $n>2$ final states for annihilations of heavy dark matter particles.

In this paper we set observational constraints of the superfluid Chaplygin gas model, which gives a unified description of the dark sector of the Universe as a Bose-Einstein condensate that behaves as dark energy while it is in the ground state and as dark matter when it is in the excited state. We first show and perform the various steps leading to a form of the equations suitable for the observational tests to be carried out. Then, by using a Markov Chain Monte Carlo code, we constrain the model with a sample of cosmology-independent long gamma-ray bursts calibrated using their type I fundamental plane, as well as the Union2.1 set and observational Hubble parameter data. In this analysis, using our cosmological constraints, we sketch the effective equation of state parameter and the deceleration parameter, and we also obtain the redshift of the transition from deceleration to acceleration $z_t$.

We propose an alternative, nonsingular, cosmic scenario based on gravitationally induced particle production. The model is an attempt to evade the coincidence and cosmological constant problems of the standard model ($\Lambda \mathrm{CDM}$) and also to connect the early and late time accelerating stages of the Universe. Our space-time emerges from a pure initial de Sitter stage thereby providing a natural solution to the horizon problem. Subsequently, due to an instability provoked by the production of massless particles, the Universe evolves smoothly to the standard radiation dominated era thereby ending the production of radiation as required by the conformal invariance. Next, the radiation becomes subdominant with the Universe entering in the cold dark matter dominated era. Finally, the negative pressure associated with the creation of cold dark matter (CCDM model) particles accelerates the expansion and drives the Universe to a final de Sitter stage. The late time cosmic expansion history of the CCDM model is exactly like in the standard $\Lambda \mathrm{CDM}$ model; however, there is no dark energy. The model evolves between two limiting (early and late time) de Sitter regimes. All the stages are also discussed in terms of a scalar field description. This complete scenario is fully determined by two extreme energy densities, or equivalently, the associated de Sitter Hubble scales connected by ${\rho }_I/{\rho }_f=(H_I/H_f{)}^2\sim {10}^{122}$, a result that has no correlation with the cosmological constant problem. We also study the linear growth of matter perturbations at the final accelerating stage. It is found that the CCDM growth index can be written as a function of the $\Lambda$ growth index, ${\gamma }_{\Lambda }\simeq 6/11$. In this framework, we also compare the observed growth rate of clustering with that predicted by the current CCDM model. Performing a ${\chi }^2$ statistical test we show that the CCDM model provides growth rates that match sufficiently well with the observed growth rate of structure.

We study the dynamics of homogeneous, isotropic universes which are governed by the Eddington-inspired alternative theory of gravity which has a single extra parameter, $\kappa$. Previous results showing singularity-avoiding behavior for $\kappa >0$ are found to be upheld in the case of domination by a perfect fluid with equation of state parameter $w>0$. The range $-\frac{1}{3}<w<0$ is found to lead to universes which experience unbounded expansion rates while still at a finite density. In the case $\kappa <0$ the addition of spatial curvature is shown to lead to the possibility of oscillation between two finite densities. Domination by a scalar field with an exponential potential is found to also lead to singularity-avoiding behavior when $\kappa >0$. Certain values of the parameters governing the potential lead to behavior in which the expansion rate of the universe changes sign several times before transitioning to regular general relativity-like behavior.

We investigate the cosmological dynamics of a nonminimally coupled scalar field system described by $F(\varphi )R$ coupling with $F(\varphi )=(1-\xi {\varphi }^N)R(N\ge 2)$ and the field potential $V(\varphi )=V_0{\varphi }^n$. We use a generic set of dynamical variables to bring out new asymptotic regimes of the underlying dynamics. However, our dynamical variables miss the most important fixed point—the de Sitter solution. We make use of the original form of the system of equations to investigate the issues related to this important solution. In particular, we show that the de Sitter solution which is a dynamical attractor of the system lies in the region of negative effective gravitational constant $G_N$, thereby leading to a ghost-dominated universe in the future and a transient quintessence (phantom) phase with $G_N>0$ around the present epoch. We also carry out a comparison of the model with other competing models of dark energy, such as Galileon-modified gravity and others.

Baryon acoustic oscillations (BAO) provide an important standard ruler which can be used to probe the recent expansion history of our Universe. We show how a simple extension of the $Om$ diagnostic, which we call $Om3$, can combine standard ruler information from BAO with standard candle information from type Ia supernovae (SNIa) to yield a powerful novel null diagnostic of the cosmological constant hypothesis. A unique feature of $Om3$ is that it requires minimal cosmological assumptions since its determination does not rely upon prior knowledge of either the current value of the matter density ${\Omega }_{0m}$ and the Hubble constant $H_0$ or the distance to the last scattering surface. Observational uncertainties in these quantities, therefore, do not affect the reconstruction of $Om3$. We reconstruct $Om3$ using the Union 2.1 SNIa data set and BAO data from SDSS, WiggleZ and 6dFGS. Our results are consistent with dark energy being the cosmological constant. We show how $Om$ and $Om3$ can be used to obtain accurate model-independent constraints on the properties of dark energy from future data sets such as BigBOSS.

We consider the three-form field, which has been considered as a candidate for realizing inflation, coupled to a scalar field which models the relativistic matter particles produced during the reheating epoch. We have investigated the stability conditions for this theory and found that introducing such a coupling does not lead to any ghosts or Laplacian instabilities. We have also investigated the reheating temperature and the production of particles due to parametric resonances. We have found that this process is more efficient in this theory compared to the result of the standard-scalar-field inflationary scenario.

Several features of an $f(R)$ theory in which there is a maximum value for the curvature are analyzed. The theory admits all the vacuum solutions of General Relativity, and also the radiation evolution for the scale factor of the standard cosmological model. Working in the Jordan frame, a complete analysis of the phase space is performed, and shown to be in agreement with examples obtained by numerical integration. In particular, nonsingular cosmological solutions were obtained, which after the bounce enter a phase of de Sitter expansion and subsequently relax to a GR-like radiation-dominated evolution.

We present a derivation of the time evolution equations for the energy content of nonhelical magnetic fields and the accompanying turbulent flows from first principles of incompressible magnetohydrodynamics in the general framework of homogeneous and isotropic turbulence. This is then applied to the early Universe, i.e., the evolution of primordial magnetic fields. Numerically integrating the equations, we find that most of the energy is concentrated at an integral wavenumber scale $k_I$ where the turbulence turn over time equals the Hubble time. At larger length scales $L$, i.e., smaller wavenumbers $q=2\pi /L\ll k_I$, independent of the assumed turbulent flow power spectrum, mode-mode coupling tends to develop a small $q$ magnetic field tail with a Batchelor spectrum proportional to the fourth inverse power of $L$ and therefore a scaling for the magnetic field of $B\sim L^{-5/2}$.

In this paper, we give a model for understanding flavor physics in the lepton sector mass hierarchy among different generations and neutrino mixing patterns. The model is constructed in the framework of supersymmetry, with a family symmetry $S4*U(1)$. There are two right-handed neutrinos introduced for a seesaw mechanism, while some standard model gauge group singlet fields are included, which transforms nontrivially under family symmetry. In the model, each order of contributions are suppressed by $\delta \sim 0.1$ compared to the previous one. In order to reproduce the mass hierarchy, $m_{\tau }$ and $\sqrt{\Delta m_{\mathrm{atm}}^2}$, and $m_{\mu }$ and $\sqrt{\Delta m_{\mathrm{sol}}^2}$ are obtained at leading order and next-to-leading order, respectively, while the electron can only get its mass through next-to-next-to-next-to-leading order contributions. For neutrino mixing angels, ${\theta }_{12}$, ${\theta }_{23}$, ${\theta }_{13}$ are 45°, 45°, 0, i.e., the bimaximal mixing pattern as a first approximation, while higher order contributions can make them consistent with experimental results. As corrections for ${\theta }_{12}$ and ${\theta }_{13}$ originate from the same contribution, there is a relation predicted for them: $\sin {\theta }_{13}=\frac{1-\tan {\theta }_{12}}{1+\tan {\theta }_{12}}$. Besides, the deviation from $\frac{\pi }{4}$ for ${\theta }_{23}$ should have been as large as the deviation from 0 for ${\theta }_{13;}$ if not, the former is suppressed by a factor of 4 compared to the latter.

We investigate the critical behavior at $\theta =\pi$ of the two-dimensional $O(3)$ nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of $\theta$, and on scaling transformations which allow a controlled analytic continuation to real values of $\theta$. Our results are compatible with a second-order phase transition, with the critical exponent of the $SU(2{)}_1$ Wess-Zumino-Novikov-Witten model, for sufficiently small values of the coupling.

The hidden photon model is one of the simplest models which can explain the anomaly of the muon anomalous magnetic moment ($g-2$). The experimental constraints, which come from the electron $g-2$ and the hydrogen transition frequencies, are studied in detail. The input parameters are set carefully in order to take dark photon contributions into account and to prevent the analysis from being self-inconsistent. It is shown that the new analysis provides a constraint severer by more than 1 order of magnitude than the previous result.

The baryon axial vector current is computed at one-loop order in large-$N_c$ baryon chiral perturbation theory, where $N_c$ is the number of colors. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference and SU(3) flavor symmetry breaking are accounted for. As expected, large-$N_c$ cancellations between different one-loop graphs are observed as a consequence of the large-$N_c$ spin-flavor symmetry of QCD baryons. Fitting our analytical formulas against experimental data on baryon semileptonic decays and the strong decays of decuplet baryons, a detailed numerical analysis regarding the determination of the basic parameters of large-$N_c$ baryon chiral perturbation theory as well as the extraction of the baryon axial vector couplings is performed. The large-$N_c$ baryon chiral perturbation theory predictions are in very good agreement both with the expectations from the $1/N_c$ expansion and with the experimental data.