For a given timelike displacement vector, the covariant Hamiltonian quasilocal energy expression requires a proper choice of reference spacetime. We propose a program for determining the reference by embedding a neighborhood of the two-sphere boundary in the dynamic spacetime into a Minkowski reference, so that the two-sphere is embedded isometrically, and then extremizing the energy to determine the embedding variables. Applying this idea to Schwarzschild spacetime, we found that for each given future timelike displacement vector our program gives a unique energy value. The static observer measures the maximal energy. Applied to the Friedmann-Lemaître-Robertson-Walker spacetime, we find that the maximum energy value is non-negative; the associated displacement vector is the unit dual mean curvature vector; and the expansion of the two-sphere boundary matches that of its reference image. For these spherically symmetric cases the reference determined by our program is equivalent to isometrically matching the geometry at the two-sphere boundary and taking the displacement vector to be orthogonal to the spacelike constant coordinate time hypersurface, like the timelike Killing vector of the Minkowski reference.

We propose a model based on radiative symmetry breaking that combines inflation with dark energy and is consistent with the Wilkinson Microwave Anisotropy Probe 7-year regions. The radiative inflationary potential leads to the prediction of a spectral index $0.955\lesssim n_S\lesssim 0.967$ and a tensor to scalar ratio $0.142\lesssim r\lesssim 0.186$, both consistent with current data but testable by the Planck experiment. The radiative symmetry breaking close to the Planck scale gives rise to a pseudo Nambu-Goldstone boson with a gravitationally suppressed mass which can naturally play the role of a quintessence field responsible for dark energy. Finally, we present a possible extra dimensional scenario in which our model could be realized.

We compute the finite-temperature and matter density corrections to the $S$-parameter at the one-loop level. At nonzero temperature $T$ and matter density $\mu$ Lorentz symmetry breaks and therefore we suggest a suitable generalization of the $S$-parameter. By computing the plasma correction, we discover a reduction of the $S$-parameter in the physically relevant region of small external momenta for any nonzero $\mu$ and $T$. In particular, the $S$-parameter vanishes at small $m/T$, where $m$ is the mass of the fermions, due to the finite extent of the temporal direction. Our results are directly applicable to the determination of the $S$-parameter via first-principle lattice simulations performed with antiperiodic boundary conditions in the temporal direction.

Under the Initial Single Pion Emission mechanism, we study the hidden-bottom dipion decays of ${\rm Y}(11020)$, i.e., ${\rm Y}(11020)\to {\rm Y}(nS){\pi }^{+}{\pi }^{-}$ ($n=1$, 2, 3) and ${\rm Y}(11020)\to h_b(mP){\pi }^{+}{\pi }^{-}$ ($m=1$, 2). We predict explicit sharp peak structures close to the $B{\overline{B}}^{*}$ and $B^{*}{\overline{B}}^{*}$ thresholds and their reflections in the ${\rm Y}(1S){\pi }^{+}$, ${\rm Y}(2S){\pi }^{+}$ and $h_b(1P){\pi }^{+}$ invariant mass spectrum distributions. We suggest that a future experiment, i.e., Belle, BABAR, and forthcoming BelleII or Super-B, carry out the search for these novel phenomena, which can provide important tests to the Initial Single Emission mechanism existing in higher bottomonia.

Motivated by the possibility that the amplitude for neutrinoless double beta decay may be much smaller than the planned sensitivity of future experiments, we study Ansätze for the neutrino mass matrix with $M_{ee}=0$. For the case in which $CP$ is conserved, we consider two classes of real-valued mass matrices: “Class I” defined by $|M_{e\mu }|=|M_{e\tau }|$, and “Class II” defined by $|M_{\mu \mu }|=|M_{\tau \tau }|$. The important phenomenological distinction between the two is that Class I permits only small values of $V_{e3}$ up to $\sim 0.03$, while Class II admits large values of $V_{e3}$ up to its empirical upper limit of 0.22. Then we introduce $CP$-violating complex phases into the mass matrix. We show that it is possible to have tribimaximal mixing with $M_{ee}=0$ and $|M_{\mu \tau }|=|M_{\mu \mu }|=|M_{\tau \tau }|$ if the Majorana phase angles are $\pm \pi /4$. Alternatively, for smaller values of $|M_{\mu \tau }|=|M_{\mu \mu }|=|M_{\tau \tau }|$ it is possible to obtain $|V_{e3}|\sim 0.2$ and generate relatively large $CP$-violating amplitudes. To eliminate phase redundancy, we emphasize rephasing any mass matrix with $M_{ee}=0$ into a standard form with two complex phases. The discussion alternates between analytical and numerical but remains purely phenomenological, without any attempt to derive mass matrices from a fundamental theory.

It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this nonquadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.

We present, in closed analytic form, a general stationary, slowly rotating black hole, which is a solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented by all possible quadratic, algebraic curvature invariants coupled to a scalar field. The solution is found as a deformation of the Schwarzschild metric in general relativity. We explicitly derive the changes to the orbital frequency at the innermost stable circular orbit and at the light ring in closed form. These results could be useful when comparing general relativity against alternative theories by (say) measurements of x-ray emission in accretion disks, or by stellar motion around supermassive black holes. When gravitational-wave astronomy comes into force, strong constraints on the coupling parameters can in principle be made.

Proton stability is one of the most perplexing puzzles in particle physics. While the renormalizable standard model forbids proton decay mediating operators due to accidental global symmetries, many of its extensions introduce such dimension four, five and six operators. Furthermore, it is, in general, expected that quantum gravity only respects local gauge, or discreet, symmetries. String theory provides the arena to study particle physics in a consistent framework of perturbative quantum gravity. An appealing proposition, in this context, is that the dangerous operators are suppressed by an Abelian gauge symmetry, which is broken near the TeV scale. A viable $U(1)$ symmetry should also be anomaly free, be family universal, and allow the generation of fermion masses via the Higgs mechanism. We discuss such $U(1)$ symmetries that arise in quasirealistic free fermionic heterotic-string derived models. Ensuring that the $U(1)$ symmetry is anomaly free at the low scale requires that the standard model spectrum is augmented by additional states that are compatible with the charge assignments in the string models. We construct such string-inspired models and discuss some of their phenomenological implications.

We construct new classes of vortexlike solutions of the $C{P}^N$ model in ($3+1$) dimensions and discuss some of their properties. These solutions are obtained by generalizing to ($3+1$) dimensions the techniques well established for the two-dimensional $C{P}^N$ models. We show that as the total energy of these solutions is infinite, they describe evolving vortices and antivortices with the energy density of some configurations varying in time. We also make some further observations about the dynamics of these vortices.

We show that the weakly turbulent instability of anti–de Sitter space, recently found in P. Bizoń and A. Rostworowski, Phys. Rev. Lett. 107, 031102 (2011) for $3+1$-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant, is present in all dimensions $d+1$ for $d\ge 3$.

In this paper, we derive Lorentz force and Maxwell’s equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to noncommutative space-time. We also show the equivalence of minimal coupling prescription and Feynman’s approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this noncommutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.

We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT correspondence to condensed matter and strongly coupled QFTs. These solutions include: (1) four- or generic ($d+2$)-dimensional solutions with planar, spherical or hyperbolic horizon topology; (2) solutions with anti-de Sitter, domain wall and Lifshitz asymptotics; (3) solutions interpolating between an anti-de Sitter spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region.

Massive gravity previously constructed as the spin-2 quantum gauge theory leads in the mass-zero limit to a modification of general relativity. As a relic from the massive theory, a vector field $v^{\lambda }$ survives which couples to the metric only. However, the coupling does not involve covariant derivatives so that $v^{\lambda }$ must be considered as four scalar fields. We analyze the static, spherically symmetric solutions of this theory. From the corresponding geodesics, we find the circular velocity profile. By interpreting this as coming from a dark density profile, the theory predicts a flat density core for $r\to 0$. But the circular velocity profile is not universal.

We introduce the surface term for quasitopological gravity in order to make the variational principle of the action well defined. We also introduce the charged black branes of quasitopological gravity and calculate the finite action through the use of the counterterm method. Then we compute the thermodynamic quantities of the black brane solution by use of Gibbs free energy and investigate the first law of thermodynamics by introducing a Smarr-type formula. Finally, we generalize our solutions to the case of rotating charged solutions.

A massive gravity theory was proposed by Visser in the late 1990s. This theory, based on a background metric $b_{\alpha \beta }$ and on an usual dynamical metric $g_{\alpha \beta }$ has the advantage of being free of ghosts as well as discontinuities present in other massive theories proposed in the past. In the present investigation, the equations of Visser’s theory are revisited with particular care on the related conservation laws. It will be shown that a multiplicative factor is missing in the graviton tensor originally derived by Visser, which has no incidence on the weak field approach but becomes important in the strong field regime when, for instance, cosmological applications are considered. In this case, contrary to some previous claims found in the literature, we conclude that a nonstatic background metric is required in order to obtain a solution able to mimic the $\Lambda \mathrm{CDM}$ cosmology.

We explore the complementarity of weak lensing and galaxy peculiar velocity measurements to better constrain modifications to General Relativity. We find no evidence for deviations from General Relativity on cosmological scales from a combination of peculiar velocity measurements (for Luminous Red Galaxies in the Sloan Digital Sky Survey) with weak lensing measurements (from the Canadian France Hawaii Telescope Legacy Survey). We provide a Fisher error forecast for a Euclid-like space-based survey including both lensing and peculiar velocity measurements and show that the expected constraints on modified gravity will be at least an order of magnitude better than with present data, i.e. we will obtain $\simeq 5\%$ errors on the modified gravity parametrization described here. We also present a model-independent method for constraining modified gravity parameters using tomographic peculiar velocity information, and apply this methodology to the present data set.

Group velocity of electromagnetic waves in plasmas derived by standard relativistic resistive magnetohydrodynamics equations is superluminal. If we assume that the group velocity represents the propagation velocity of a signal, we have to worry about the causality problem. That is, some acausal phenomena may be induced, such as information transportation to the absolute past and a spontaneous decrease in the entropy. Here, we tried to find the acausal phenomena using standard relativistic resistive magnetohydrodynamics numerical simulations in the suggested situation of the acausal phenomena. The calculation results showed that even in such situations no acausal effect happens. The numerical result with respect to the velocity limit of the information transportation is consistent with a linear theory of wave train propagation. Our results assure that we can use these equations without the problems of acausal phenomena.

Classical scalar fields have been proposed as possible candidates for the dark matter component of the universe. Given the fact that supermassive black holes seem to exist at the center of most galaxies, in order to be a viable candidate for the dark matter halo a scalar field configuration should be stable in the presence of a central black hole, or at least be able to survive for cosmological time scales. In the present work we consider a scalar field as a test field on a Schwarzschild background, and study under which conditions one can obtain long-lived configurations. We present a detailed study of the Klein-Gordon equation in the Schwarzschild space-time, both from an analytical and numerical point of view, and show that indeed there exist quasistationary solutions that can remain surrounding a black hole for large time scales.

We reconsider Higgs boson invisible decays into Dark Matter in the light of recent Higgs searches at the LHC. Present hints in the Compact Muon Solenoid and ATLAS data favor a nonstandard Higgs boson with approximately 50% invisible branching ratio, and mass around 143 GeV. This situation can be realized within the simplest thermal scalar singlet Dark Matter model, predicting a Dark Matter mass around 50 GeV and direct detection cross section just below present bound. The present runs of the Xenon100 and LHC experiments can test this possibility.

The mass and decay constant of the ground state of spin-singlet $b\overline{b}$ is calculated by using the QCD sum rules method. This meson is an axial vector $P$ wave named $h_b(1P)$ meson with $J^P=1^{+}$. It is found that the mass of this meson is $m=(9940\pm 37)\mathrm{MeV}$, which is consistent with the recent experimental data by the Belle Collaboration.