The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this paper we construct an improved parametrized version of the method, and discuss some subtleties in its application related to secular motions in first as well as in higher-order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.

The present paper is devoted to the analysis of cosmological solutions and its stability in the frame of $F(R)$ Hořava-Lifshitz gravity. The perturbations around general spatially flat Friedmann-Lemaître-Robertson-Walker solutions are analyzed and it is shown that the stability of those solutions depends on the type of theory, i.e. on the form of the action $F(R)$, as well as on the extra parameters contained in every Hořava-Lifshitz theory (due to the breaking of Lorentz invariance). The (in)stability of cosmological solutions can provide a constraint of the models and it may give new observational predictions. A natural explanation of the end of inflation and radiation/matter phases can be provided by this class of theories. An explicit example of $F(R)$ gravity is studied, and the transition between the different epochs of the Universe history is achieved.

The ‘‘effective geometry” formalism is used to study the perturbations of a white dwarf described as a self-gravitating fermion gas with a completely degenerate relativistic equation of state of barotropic type. The quantum nature of the system causes an absence of homological properties, manifested instead by polytropic stars, and requires a parametric study of the solutions both at the numerical and analytical level. We have explicitly derived a compact analytical parametric approximate solution of Padé type, which gives density curves and stellar radii in good accordance with already existing numerical results. After validation of this new type of approximate solutions, we use them to construct the effective acoustic metric governing general perturbations following Chebsch’s formalism. Even in this quantum case, the stellar surface exhibits a curvature singularity due to the vanishing of density, as already evidenced in past studies on nonquantum self-gravitating polytropic stars. The equations of the theory are finally numerically integrated in the simpler case of irrotational spherical pulsating perturbations, including the effect of backreaction, in order to have a dynamical picture of the process occurring in the acoustic metric.

In the standard model, custodial symmetry is violated by the hypercharge U(1) gauge interactions and the Yukawa couplings, while being preserved by the Higgs scalar potential. In the two-Higgs-doublet model (2HDM), the generic scalar potential introduces new sources of custodial symmetry breaking. We obtain a basis-independent expression for the constraints that impose custodial symmetry on the 2HDM scalar potential. These constraints impose $CP$-conservation on the scalar potential and vacuum, and in addition add one extra constraint on the scalar potential parameters. We clarify the mass degeneracies of the 2HDM that arise as a consequence of the custodial symmetry. We also provide a computation of the oblique parameters ($S$, $T$, and $U$) for the most general $CP$-violating 2HDM in the basis-independent formalism. We demonstrate that the 2HDM contributions to $T$ and $U$ vanish in the custodial symmetry limit, as expected. Using the experimental bounds on $S$ and $T$ from precision electroweak data, we examine the resulting constraints on the general 2HDM parameter space.

We reanalyze the prompt muon neutrino flux from gamma-ray bursts (GRBs) in terms of the particle physics involved, as in the example of the often-used reference Waxman-Bahcall GRB flux. We first reproduce this reference flux explicitly treating synchrotron energy losses of the secondary pions. Then we include additional neutrino production modes, the neutrinos from muon decays, the magnetic field effects on all secondary species, and flavor mixing with the current parameter uncertainties. We demonstrate that the combination of these effects modifies the shape of the original Waxman-Bahcall GRB flux significantly and changes the normalization by a factor of 3 to 4. As a consequence, the gamma-ray burst search strategy of neutrino telescopes may be based on the wrong flux shape, and the constraints derived for the GRB neutrino flux, such as the baryonic loading, may in fact be much stronger than anticipated.

We report on a potentially new class of non-Fermi liquids in ($2+1$)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.

We present simple new approximate formulas, for both scalar and spinor QED, for the number of particles produced from vacuum by a time-dependent electric field, incorporating the interference effects that arise from an arbitrary number of distinct semiclassical turning points. Such interference effects are important when the temporal profile of the laser pulse has subcycle structure. We show how the resulting semiclassical intuition may be used to guide the design of temporal profiles that enhance the momentum spectrum due to interference effects. The result is easy to implement and generally applicable to time-dependent tunneling problems, such as those that appear in many other contexts in particle and nuclear physics, condensed matter physics, atomic physics, chemical physics, and gravitational physics.

The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson’s. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants and show that the gravitational wave stress-energy tensor still reduces to Isaacson’s. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.

The calculation of the self force in the modeling of the gravitational-wave emission from extreme-mass-ratio binaries is a challenging task. Here we address the question of the possible emergence of a persistent spurious solution in time-domain schemes, referred to as a Jost junk solution in the literature, that may contaminate self-force calculations. Previous studies suggested that Jost solutions are due to the use of zero initial data, which is inconsistent with the singular sources associated with the small object, described as a point mass. However, in this work we show that the specific origin is an inconsistency in the translation of the singular sources into jump conditions. More importantly, we identify the correct implementation of the sources at late times as the sufficient condition guaranteeing the absence of Jost junk solutions.

We calculate the cross section for diffractive hadron production in deep inelastic scattering off heavy nuclei in the framework of gluon saturation/color glass condensate. We analyze the kinematic region of the future Electron-Ion Collider. We argue that coherent and incoherent diffractive channels are very sensitive to the structure of the nuclear matter at low $x$. This expresses itself in a characteristic dependence of the cross sections on rapidity and transverse momentum of the produced hadron and on the nuclear weight. We also discuss dependence on the scattering angle and argue that both coherent and incoherent cross sections may be within experimental reach at Electron-Ion Collider.

We report the first observation of two Cabibbo-suppressed decay modes of the $B_s^0$ meson. Using a sample of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ corresponding to $5.9{\mathrm{fb}}^{-1}$ of integrated luminosity collected with the CDF II, the collider detector at the Fermilab Tevatron, we search for new $B_s^0$ decay modes in a sample of events containing $J/\psi \to {\mu }^{+}{\mu }^{-}$ decays. We reconstruct a $B_s^0\to J/\psi K^{*}(892{)}^0$ signal with $K^{*}(892{)}^0\to K^{+}{\pi }^{-}$, observing a yield of $151\pm 25$ events with a statistical significance of $8.0\sigma$. We also reconstruct a $B_s^0\to J/\psi K_S^0$ signal with $K_S^0\to {\pi }^{+}{\pi }^{-}$, observing a yield of $64\pm 14$ events with a statistical significance of $7.2\sigma$. From these yields, we extract the branching ratios $\mathcal{B}(B_s^0\to J/\psi K^{*}(892{)}^0)=(8.3\pm 3.8)\times {10}^{-5}$ and $\mathcal{B}(B_s^0\to J/\psi K^0)=(3.5\pm 0.8)\times {10}^{-5}$, where statistical, systematic, and fragmentation-fraction uncertainties are included in the combined uncertainty.

We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint, which arises from the reparametrization invariance of the particle orbit. As the necessary and sufficient condition for the existence of a constant of motion, we obtain a set of equations with a hierarchical structure, which is understood as a generalization of the Killing tensor equation. It is also a generalization of the conventional argument in that it includes the case when the conservation condition holds only on the constraint surface in the phase space. In that case, it is shown that the constant of motion is associated with a conformal Killing tensor. We apply the hierarchical equations and find constants of motion in the case of a charged particle in an electromagnetic field in black hole spacetimes. We also demonstrate that gravitational and electromagnetic fields exist in which a charged particle has a constant of motion associated with a conformal Killing tensor.

Dynamical issues associated with quantum fields in Rindler space are addressed in a study of the interaction between two sources at rest generated by the exchange of scalar particles, photons, and gravitons. These static interaction energies in Rindler space are shown to be scale invariant, complex quantities. The imaginary part will be seen to have its quantum mechanical origin in the presence of an infinity of zero modes in uniformly accelerated frames which in turn are related to the radiation observed in inertial frames. The impact of a uniform acceleration on the stability of matter and the properties of particles is discussed, and estimates are presented of the instability of hydrogen atoms when approaching the horizon.

General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength 2-form and induction 2-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory predictive and physically interpretable. Taking into account the higher-order polynomial dispersion relation and associated causal structure of general linear electrodynamics, we carefully develop its Hamiltonian formulation from first principles. Canonical quantization of the resulting constrained system then results in a quantum vacuum which is sensitive to the constitutive tensor of the classical theory. As an application we calculate the Casimir effect in a birefringent linear optical medium.

We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current “best model of inflation.” The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power $p>4$ are strongly disfavored. The class of small field models as a whole has posterior odds of approximately $3:1$ when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model.

Using strong lensing data, Milgrom’s modified Newtonian dynamics (MOND) and its covariant TeVeS (tensor-vector-scalar theory) are examined here as an alternative to the conventional $\Lambda \mathrm{CDM}$ paradigm. We examine 10 double-image, gravitational lensing systems in which the lens masses have been estimated by stellar population synthesis models. While mild deviations exist, we find no strong case of outliers to the TeVeS theory.

A dual-Regge model with a nonlinear proton Regge trajectory in the missing mass $(M_X^2)$ channel, describing the experimental data on low-mass single diffraction dissociation (SDD), is constructed. Predictions for the LHC energies are given.

Lepton flavor violation in $\tau$ and $\mu$ processes is studied in the littlest Higgs model with $T$ parity. We consider various asymmetries defined in polarized $\tau$ and $\mu$ decays. Correlations among branching ratios and asymmetries are shown in the following lepton flavor violation processes: ${\mu }^{+}\to e^{+}\gamma$, ${\mu }^{+}\to e^{+}{e}^{+}{e}^{-}$, ${\mu }^{-}A\to e^{-}A$ ($A=\mathrm{Al}$, Ti, Au, and Pb), ${\tau }^{+}\to {\mu }^{+}\gamma$, ${\tau }^{+}\to {\mu }^{+}{\mu }^{+}{\mu }^{-}$, ${\tau }^{+}\to {\mu }^{+}{e}^{+}{e}^{-}$, ${\tau }^{+}\to {\mu }^{+}P$ ($P={\pi }^0$, $\eta$ and ${\eta }^{\prime }$), ${\tau }^{+}\to {\mu }^{+}V$ ($V={\rho }^0$, $\omega$ and $\varphi$), ${\tau }^{+}\to e^{+}\gamma$, ${\tau }^{+}\to e^{+}{e}^{+}{e}^{-}$, ${\tau }^{+}\to e^{+}{\mu }^{+}{\mu }^{-}$, ${\tau }^{+}\to e^{+}P$, ${\tau }^{+}\to e^{+}V$, ${\tau }^{+}\to {\mu }^{+}{\mu }^{+}{e}^{-}$ and ${\tau }^{+}\to e^{+}{e}^{+}{\mu }^{-}$. It is shown that large parity asymmetries and time-reversal asymmetries are allowed in ${\mu }^{+}\to e^{+}{e}^{+}{e}^{-}$. For $\tau$ lepton flavor violation processes, sizable asymmetries are possible reflecting characteristic chirality structure of lepton flavor violating interactions in this model.

Using the canonical method, we investigate the Dp-brane world-volume noncommutativity in a weakly curved background. The term “weakly curved” means that, in the leading order, the source of nonflatness is an infinitesimally small Kalb-Ramond field $B_{\mu \nu }$, linear in coordinate, while the Ricci tensor does not contribute, being an infinitesimal of the second order. On the solution of boundary conditions, we find a simple expression for the space-time coordinates in terms of the effective coordinates and momenta. This basic relation helped us to prove that noncommutativity appears only on the world sheet boundary. The noncommutativity parameter has a standard form, but with the infinitesimally small and coordinate-dependent antisymmetric tensor $B_{\mu \nu }$. This result coincides with that obtained on the group manifolds in the limit of the large level $n$ of the current algebra. After quantization, the algebra of the functions on the Dp-brane world volume is represented with the Kontsevich star product instead of the Moyal one in the flat background.

We show that in theories of generalized teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also argue that these theories appear to have extra degrees of freedom with respect to general relativity. The usual teleparallel Lagrangian, which has been extensively studied and leads to a theory dynamically equivalent to general relativity, is an exception. Both of these facts appear to have been overlooked in the recent literature on $f(T)$ gravity, but are crucial for assessing the viability of these theories as alternative explanations for the acceleration of the Universe.