We discuss several features of the propagation of perturbations in nonlinear scalar field theories using the effective metric. It is shown that the effective metric can be classified according to whether the gradient of the scalar field is timelike, null, or spacelike, and this classification is illustrated with two examples. We shall also show that different signatures for the effective metric are allowed.

We develop a theoretical framework to study slowly rotating compact stars in a rather general class of alternative theories of gravity, with the ultimate goal of investigating constraints on alternative theories from electromagnetic and gravitational-wave observations of compact stars. Our Lagrangian includes as special cases scalar-tensor theories (and indirectly $f(R)$ theories) as well as models with a scalar field coupled to quadratic curvature invariants. As a first application of the formalism, we discuss (for the first time in the literature) compact stars in Einstein-Dilaton-Gauss-Bonnet gravity. We show that compact objects with central densities typical of neutron stars cannot exist for certain values of the coupling constants of the theory. In fact, the existence and stability of compact stars sets more stringent constraints on the theory than the existence of black hole solutions. This work is a first step in a program to systematically rule out (possibly using Bayesian model selection) theories that are incompatible with astrophysical observations of compact stars.

In light of the surge in popularity of electromagnetic cloaking devices, we consider whether it is possible to use general relativity to cloak a volume of spacetime through gravitational lensing. We explore the cloaking properties of a spacetime through a ray-tracing procedure, wherein we plot the spatial trajectories of a congruence of initially parallel null geodesics as they cross the geometry. In this context, a cloaking device would cause all of the null geodesics in an initially parallel congruence incident upon the cloaking geometry to circumnavigate an internal region, and as the geodesics emerge from the geometry, they regain their original configuration. Thus, if gravitational lensing were used as a mechanism for cloaking, the internal region would be causally isolated from the external spacetime. For this reason, we propose an effective cloaking geometry wherein (only) most of ingoing null geodesics will splay away from a central region, and then regain their initial configuration as they exit the geometry. Thus, a compact object sitting within the effective cloaking geometry will impede a smaller cross section of the null congruence, and therefore appear optically smaller from all sides. We build our effective cloaking geometry by connecting a Minkowski spacetime exterior to a spherically symmetric, curved spacetime along a timelike hypersurface of constant radius using the Israel junction conditions. The junction conditions require a shell of matter of infinitesimal width confined to the junction surface. The matter required to build such a spacetime must violate the null energy condition.

We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup, the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional piecewise linear spaces, with the solutions to the lattice equations providing a suitable approximation to the continuum wave functional. The equations incorporate a set of constraints on the quantum wave functional, arising from the triangle inequalities and their higher-dimensional analogs. The character of the solutions is discussed in the strong-coupling (large-$G$) limit, where it is shown that the wave functional only depends on geometric quantities, such as areas and volumes. An explicit form, determined from the discrete wave equation supplemented by suitable regularity conditions, shows peaks corresponding to integer multiples of a fundamental unit of volume. An application of the variational method using correlated product wave functions suggests a relationship between quantum gravity in $n+1$ dimensions, and averages computed in the Euclidean path integral formulation in $n$ dimensions. The proposed discrete equations could provide a useful, and complementary, computational alternative to the Euclidean lattice path integral approach to quantum gravity.

We perform fully general relativistic simulations to address the inspiral and merger of binary white dwarf–neutron stars. The initial binary is in a circular orbit at the Roche critical separation. The goal is to determine the ultimate fate of such systems. We focus on binaries whose total mass exceeds the maximum mass ($M_{\max }$) a cold, degenerate equation of state can support against gravitational collapse. The time and length scales span many orders of magnitude, making fully general relativistic hydrodynamic simulations computationally prohibitive. For this reason, we model the white dwarf as a “pseudo—white dwarf” as in our binary white dwarf–neutron star (WDNS) head-on collisions study [V. Paschalidis, Z. Etienne, Y. T. Liu, and S. L. Shapiro, Phys. Rev. D 83, 064002 (2011)]. Our general relativistic hydrodynamic simulations of a pseudo-WDNS (pWDNS) system with a $0.98M_{\odot }$ white dwarf and a $1.4M_{\odot }$ neutron star show that the merger remnant is a spinning Thorne-Zytkow-like object (TZlO) surrounded by a massive disk. The final total rest mass exceeds $M_{\max }$, but the remnant does not collapse promptly. To assess whether the object will ultimately collapse after cooling, we introduce radiative thermal cooling. We first apply our cooling algorithm to TZlOs formed in pWDNS head-on collisions, and show that these objects collapse and form black holes on the cooling time scale, as expected. However, when we cool the spinning TZlO formed in the merger of a circular-orbit pWDNS binary, the remnant does not collapse, demonstrating that differential rotational support is sufficient to prevent collapse. Given that the final total mass exceeds $M_{\max }$ for our cold equation of state, magnetic fields and/or viscosity may redistribute angular momentum, ultimately leading to delayed collapse to a black hole. We infer that the merger of realistic massive WDNS binaries likely will lead to the formation of spinning TZlOs that undergo delayed collapse.

One of the deepest and most long-standing mysteries in physics has been the huge discrepancy between the observed vacuum density and our expectations from theories of high energy physics, which has been dubbed the old cosmological constant problem. One proposal to address this puzzle at the semiclassical level is to decouple quantum vacuum from spacetime geometry via a modification of gravity that includes an incompressible fluid, known as gravitational aether. In this paper, we discuss classical predictions of this theory along with its compatibility with cosmological and experimental tests of gravity. We argue that deviations from general relativity (GR) in this theory are sourced by pressure or vorticity. In particular, the theory predicts that the gravitational constant for radiation is 33% larger than that of nonrelativistic matter, which is preferred by (most) cosmic microwave background (CMB), Ly-$\alpha$ forest, and ${}^7\mathrm{Li}$ primordial abundance observations, while being consistent with other cosmological tests at $\sim 2\sigma$ level. It is further shown that all parametrized post-newtonian parameters have the standard GR values aside from the anomalous coupling to pressure ${\zeta }_4$, which has not been directly measured. A more subtle prediction of this model (assuming irrotational aether) is that the (intrinsic) gravitomagnetic effect is 33% larger than GR prediction. This is consistent with current limits from LAGEOS and Gravity Probe B at $\sim 2\sigma$ level.

The symmetron is a scalar field associated with the dark sector whose coupling to matter depends on the ambient matter density. The symmetron is decoupled and screened in regions of high density, thereby satisfying local constraints from tests of gravity, but couples with gravitational strength in regions of low density, such as the cosmos. In this paper we derive the cosmological expansion history in the presence of a symmetron field, tracking the evolution through the inflationary, radiation- and matter-dominated epochs, using a combination of analytical approximations and numerical integration. For a broad range of initial conditions at the onset of inflation, the scalar field reaches its symmetry-breaking vacuum by the present epoch, as assumed in the local analysis of spherically symmetric solutions and tests of gravity. For the simplest form of the potential, the energy scale is too small for the symmetron to act as dark energy, hence we must add a cosmological constant to drive late-time cosmic acceleration. We briefly discuss a class of generalized, nonrenormalizable potentials that can have a greater impact on the late-time cosmology, though cosmic acceleration requires a delicate tuning of parameters in this case.

One of the main goals of modern cosmology remains to summon up a self-consistent policy, able to explain, in the framework of Einstein’s theory, the cosmic speedup and the presence of dark matter in the Universe. According to the holographic principle, which postulates the existence of a minimal size of a physical region, we argue, in this paper, that if this size exists for the Universe and it is accrued from the independent geometrical second order invariants, it would be possible to ensure a surprising source for dark matter and a viable candidate for explaining the late acceleration of the Universe. We develop low redshift tests, such as supernovae Ia and kinematical analysis, compiled by the use of cosmography, and we compare the outcomes with higher redshift tests, such as the CMB peak and anisotropy of the cosmic power spectrum. All the results indicate that the models presented here can be interpreted as unified models that are capable of describing both dark matter and dark energy.

To constrain cosmological parameters, one often makes a joint analysis with different combinations of observational data sets. In this paper we take the figure of merit (FoM) for Dark Energy Task Force fiducial model (Chevallier-Polarski-Linder model) to estimate goodness of different combinations of data sets, which include 11 widely used observational data sets (type Ia supernovae, observational hubble parameter, baryon acoustic oscillation, cosmic microwave background, x-ray cluster baryon mass fraction, and gamma-ray bursts). We analyze different combinations and make a comparison for two types of combinations based on two types of basic combinations, which are often adopted in the literature. We find two sets of combinations, which have a strong ability to constrain the dark energy parameters: one has the largest FoM, and the other contains less observational data with a relatively large FoM and a simple fitting procedure.

We examine the constraints on the luminosity-dependent density evolution model for the evolution of blazars given the observed spectrum of the diffuse gamma-ray background (DGRB), blazar source-count distribution, and the blazar spectral energy distribution sequence model, which relates the observed blazar spectrum to its luminosity. We show that the DGRB observed by the Large Area Telescope (LAT) aboard the Fermi Gamma-Ray Space Telescope can be produced entirely by gamma-ray emission from blazars and nonblazar active galactic nuclei, and that our blazar evolution model is consistent with and constrained by the spectrum of the DGRB and flux source-count distribution function of blazars observed by Fermi-LAT. Our results are consistent with previous work that used EGRET spectral data to forecast the Fermi-LAT DGRB. The model includes only three free parameters, and forecasts that $\gtrsim 95\%$ of the flux from blazars will be resolved into point sources by Fermi-LAT with 5 years of observation, with a corresponding reduction of the flux in the DGRB by a factor of $\sim 2$ to 3 (95% confidence level), which has implications for the Fermi-LAT’s sensitivity to dark matter annihilation photons.

Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluza-Klein modes in extension of the standard model with a warped extra dimension and the custodial symmetry $SU(3{)}_c\times SU(2{)}_L\times SU(2{)}_R\times U(1{)}_X\times P_{LR}$. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluza-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infinite series of Kaluza-Klein excitations in a universal extra dimension. Furthermore, we analyze the possible connection between the propagators in five-dimensional full theory and the product of bulk profiles with corresponding propagators of exciting Kaluza-Klein modes in four-dimensional effective theory, and recover some relations presented in the literature for warped and universal extra dimensions, respectively. As an example, we present the correction from new physics to the branching ratio of $\overline{B}\to X_s\gamma$ to the order $\mathcal{O}({\mu }_{\mathrm{EW}}^2/{\Lambda }_{\mathrm{KK}}^2)$ in extension of the standard model with a warped extra dimension and the custodial symmetry, where ${\Lambda }_{\mathrm{KK}}$ denotes the energy scale of low-lying Kaluza-Klein excitations and ${\mu }_{\mathrm{EW}}$ denotes the electroweak energy scale.

Theoretical predictions for the $pp\to 2J/\psi +X$ cross section at $\sqrt{s}=7\mathrm{TeV}$ with different kinematical restrictions are presented. Results are compared with the first LHCb data available. Special attention is paid to a possible signal from novel particles—tetraquarks build from two valence $c$-quarks and two valence $\overline{c}$-quarks. According to our estimates, it is quite possible to observe at least one of these states (tensor tetraquark) experimentally under LHCb conditions.

The nonlinear Balitsky-Kovchegov equation at small $x$ is solved numerically, incorporating impact parameter dependence. Confinement is modeled by including effective gluon mass in the dipole evolution kernel, which regulates the splitting of dipoles with large sizes. It is shown that the solution is sensitive to different implementations of the mass in the kernel. In addition, running coupling effects are taken into account in this analysis. Finally, a comparison of the calculations using the dipole framework with the inclusive data from HERA on the structure functions $F_2$ and $F_L$ is performed.

A fourth generation of quarks, if it exists, may provide sufficient $CP$ violation for the baryon asymmetry of the Universe. We estimate the neutron electric dipole moment in the presence of a fourth generation and find it would be dominated by the strange quark chromoelectric dipole moment, assuming it does not get wiped out by a Peccei-Quinn symmetry. Both the three electroweak loop and the two-loop electroweak/one-loop gluonic contributions are considered. With $m_{b^{\prime }}$, $m_{t^{\prime }}$ at 500 GeV or so that can be covered at the LHC, and with a Jarlskog $CP$ violation factor that is consistent with hints of New Physics in $b\to s$ transitions, the neutron electric dipole moment is found around ${10}^{-31}e\mathrm{cm}$, still far below the ${10}^{-28}e\mathrm{cm}$ reach of the new experiments being planned or under construction.

In this paper we will analyze a noncommutative deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in $N=1$ superspace formalism. We will then analyze the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for this deformed ABJM theory, and its linear as well as nonlinear gauges. We will show that the sum of the gauge fixing term and the ghost term for this deformed ABJM theory can be expressed as a combination of the total BRST and the total anti-BRST variation, in Landau and nonlinear gauges. We will show that in Landau and Curci-Ferrari gauges deformed ABJM theory is invariant under an additional set of symmetry transformations. We will also discuss the effect that the addition of a bare mass term has on this theory.

Our goal will be the description of a theory of Gribov’s type as a physical process of phase transition in the context of a spontaneous symmetry breaking. We mainly focus at the quantum stability of the whole process.

Based on the strong coupling expansion, we reinvestigate the two-dimensional $O(N)$ sigma model by the use of Padé-Borel approximants. The conventional strong coupling expansion of the mass square $M$ in momentum space in $\beta =1/g^2$ is inverted to give $\beta$ expanded in $1/M$. Borel transform of $\beta$ with respect to $M$ is carried out and the result is improved as the rational function by the Padé method. We find the behavior of Padé-Borel transformed bare coupling at 18th order is consistent for $N\ge 3$ with that of continuum scaling to the four-loop perturbation theory. We estimate the nonperturbative mass gap at $N\ge 3$ and find agreement with the exact result by Hasenfratz et. al.

We describe a class of exactly soluble semiclassical models for gravitational collapse obtained by patching dynamical spherically symmetric exterior space-times with cosmological interior space-times. These are generalizations of the Oppenheimer-Snyder type models to include classical and quantum scalar fields as sources for the interior metric, and null fluids with pressure as sources for the exterior metric. The polymer quantization method is used for the scalar field. The resulting semiclassical metrics exhibit novel features such as evaporating horizons and singularity avoidance.

It has recently been argued by Copeland et al. that in 11 dimensions two orbifold planes can collide and bounce in a regular way, even when the bulk metric is perturbed away from Milne spacetime to a Kasner solution. In this paper, we point out that as a consequence the global phoenix structure of the cyclic universe is significantly enriched. Spatially separated regions, with different density fluctuation amplitudes as well as different non-Gaussian characteristics, are all physically realized. Those regions containing by far the most structure are specified by a fluctuation amplitude of $Q\sim {10}^{-4.5}$ and local non-Gaussianity parameters $f_{\mathrm{NL}}\sim \mathcal{O}(\pm 10)$ and $g_{\mathrm{NL}}\sim \mathcal{O}(-{10}^3)$, in agreement with current observations.

Lepton number violation can be induced by Majorana neutrinos in four-body decays of the neutral $B$ meson and the top quark. We study the effects of Majorana neutrinos in these $|\Delta L|=2$ decays in a scenario where a single heavy neutrino can enhance the amplitude via the resonant mechanism. Using current bounds on heavy neutrino mixings, the most optimistic branching ratios turn out to be at the level of ${10}^{-6}$ for ${\overline{B}}^0\to D^{+}{e}^{-}{e}^{-}{\pi }^{+}$ and $t\to b{l}^{+}{l}^{+}{W}^{-}$ decays. Searches for these lepton number violation decays at future facilities can provide complementary constraints on masses and mixings of Majorana neutrinos.