The intersection of the ten-dimensional fuzzy conifold $Y_F^{10}$ with $S_F^5\times S_F^5$ is the compact eight-dimensional fuzzy space $X_F^8$. We show that $X_F^8$ is (the analogue of) a principal $U(1)\times U(1)$ bundle over fuzzy $SU(3)/(U(1)\times U(1))(\equiv {\mathcal{M}}_F^6)$. We construct ${\mathcal{M}}_F^6$ using the Gell-Mann matrices by adapting Schwinger’s construction. The space ${\mathcal{M}}_F^6$ is of relevance in higher dimensional quantum Hall effect and matrix models of $D$-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of $SU(3)$ eigenvectors. We construct the Dirac operator on ${\mathcal{M}}_F^6$ from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

Schwinger pair creation in a purely time-dependent electric field can be described through a quantum Vlasov equation describing the time evolution of the single-particle momentum distribution function. This equation exists in two versions, both of which can be derived by a Bogoliubov transformation, but whose equivalence is not obvious. For the spinless case, we show here that the difference between these two evolution equations corresponds to the one between the “in-out” and “in-in” formalisms. We give a simple relation between the asymptotic distribution functions generated by the two Vlasov equations. As examples we discuss the Sauter and single-soliton field cases.

We study the Boltzmann equation with elastic pointlike scalar interactions in two different versions of the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the nonrenormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one also has access to the nonapproximated result for comparison.

Finsler geometry is a well-known generalization of Riemannian geometry which allows us to account for a possibly nontrivial structure of the space of configurations of relativistic particles. Here we establish a link between Finsler geometry and the sorts of models with curved momentum space and doubly special relativistic relativistic symmetries which have been of interest recently in the quantum-gravity literature. We use as a case study the much-studied scenario which is inspired by the $\kappa$-Poincaré quantum group and show that the relevant deformation of relativistic symmetries can be implemented within a Finsler geometry.

Certain scalar-tensor theories have the property of endowing stars with scalar hair, sourced either by the star’s own compactness (spontaneous scalarization) or, for binary systems, by the companion’s scalar hair (induced scalarization) or by the orbital binding energy (dynamical scalarization). Scalarized stars in binaries present different conservative dynamics than in general relativity, and can also excite a scalar mode in the metric perturbation that carries away dipolar radiation. As a result, the binary orbit shrinks faster than predicted in general relativity, modifying the rate of decay of the orbital period. In spite of this, scalar-tensor theories can pass existing binary pulsar tests, because observed pulsars may not be compact enough or sufficiently orbitally bound to activate scalarization. Gravitational waves emitted during the last stages of compact binary inspirals are thus ideal probes of scalarization effects. For the standard projected sensitivity of advanced LIGO, we here show that, if the neutron star equation of state is such that the stars can be sufficiently compact that they enter the detector’s sensitivity band already scalarized, then gravitational waves could place constraints at least comparable to binary pulsars. If the stars dynamically scalarize while inspiraling in band, then constraints are still possible provided the equation of state leads to scalarization that occurs sufficiently early in the inspiral, roughly below an orbital frequency of 50 Hz. In performing these studies, we rederive an easy-to-calculate data analysis measure, an integrated phase difference between a general-relativistic and a modified signal, and connect it directly to the Bayes factor, showing that it can be used to determine whether a modified gravity effect is detectable. Finally, we find that custom-made templates are equally effective as model-independent, parametrized post-Einsteinian waveforms at detecting such modified gravity effects at realistic signal-to-noise ratios.

The detailed calculations of the energy in the ghost-free massive gravity theory are presented. The energy is defined in the standard way within the canonical approach, but to evaluate it requires resolving the Hamiltonian constraints, which are known, in general, only implicitly. Fortunately, the constraints can be explicitly obtained and resolved in the spherically symmetric sector, which allows one to evaluate the energy. It turns out that the energy is positive for globally regular and asymptotically flat fields constituting the “physical sector” of the theory. In other cases the energy can be negative and even unbounded from below, which suggests that the theory could still be plagued with ghost instability. However, a detailed inspection reveals that the corresponding solutions of the constraints are either not globally regular or not asymptotically flat. Such solutions cannot describe initial data triggering ghost instability of the physical sector. This allows one to conjecture that the physical sector could actually be protected from the instability by a potential barrier separating it from negative energy states.

We study the origin of dark matter based on the ghost-free bigravity theory with twin matter fluids. The present cosmic acceleration can be explained by the existence of graviton mass, while dark matter is required in several cosmological situations (the galactic missing mass, the cosmic structure formation and the cosmic microwave background observation). Assuming that the Compton wavelength of the massive graviton is shorter than a galactic scale, we show the bigravity theory can explain dark matter by twin matter fluid as well as the cosmic acceleration by tuning appropriate coupling constants.

The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by performing numerical simulations within the full Einstein-Maxwell theory. We take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$ and charge $Q$. Evolutions are performed to scan this parameter space within the intervals $0\le a/M\le 0.994$ and $0\le Q/M\le 0.996$, corresponding to an extremality parameter $a/a_{\max }$ ($a_{\max }\equiv \sqrt{M^2-Q^2}$) ranging from 0 to 0.995. These KNBHs are evolved, together with a small bar-mode perturbation, up to a time of order $120M$. Our results suggest that for small $Q/a$, the quadrupolar oscillation modes depend solely on $a/a_{\max }$, a universality also apparent in previous perturbative studies in the regime of small rotation. Using as a stability criterion the absence of significant relative variations in the horizon areal radius and BH spin, we find no evidence for any developing instability.

In this paper, we present a deformed model of Einstein-Proca spacetime based on the replacement of pointlike sources by noncommutative smeared distributions. We discuss the solutions to the set of noncommutative Einstein-Proca equations thus obtained, with emphasis on the issue of singularities and horizons.

We study various aspects of black holes and gravitational collapse in Einstein-Yang-Mills theory under the assumption of spherical symmetry. Numerical evolution on hyperboloidal surfaces extending to future null infinity is used. We begin by constructing colored and Reissner-Nordström black holes on surfaces of constant mean curvature and analyze their perturbations. These linearly perturbed black holes are then evolved into the nonlinear regime and the masses of the final Schwarzschild black holes are computed as a function of the initial horizon radius. We compare with an information-theoretic bound on the lifetime of unstable hairy black holes derived by Hod. Finally we study critical phenomena in gravitational collapse at the threshold between different Yang-Mills vacuum states of the final Schwarzschild black holes, where the $n=1$ colored black hole forms the critical solution. The work of Choptuik et al. [Phys. Rev. D 60, 124011 (1999)] is extended by using a family of initial data that includes another region in parameter space where the colored black hole with the opposite sign of the Yang-Mills potential forms the critical solution. We investigate the boundary between the two regions and discover that the Reissner-Nordström solution appears as a new approximate codimension-two attractor.

In this paper, we consider the propagation of scalar particles in a higher-dimensional Schwarzschild–de Sitter black-hole spacetime, both on the brane and in the bulk. Our analysis applies for arbitrary partial modes and for both minimal and nonminimal coupling of the scalar field. A general expression for the greybody factor is analytically derived in each case, and its low-energy behavior is studied in detail. Its profile in terms of scalar properties (angular-momentum number and nonminimal coupling parameter) and spacetime properties (number of extra dimensions and cosmological constant) is thoroughly investigated. In contrast to previous studies, the effect of the cosmological constant is taken into account both close to and far away from the black-hole horizon. The dual role of the cosmological constant, that may act either as a helping agent to the emission of scalar particles or as a deterring effect depending on the value of the nonminimal coupling parameter, is also demonstrated.

In this paper, we study the quantization of the ($1+1$)-dimensional projectable Hořava-Lifshitz (HL) gravity, and find that, when only gravity is present, the system can be quantized by following the canonical Dirac quantization, and the corresponding wave function is normalizable for some orderings of the operators. The corresponding Hamilton can also be written in terms of a simple harmonic oscillator, whereby the quantization can be carried out quantum mechanically in the standard way. When the HL gravity minimally couples to a scalar field, the momentum constraint is solved explicitly in the case where the fundamental variables are functions of time only. In this case, the coupled system can also be quantized by following the Dirac process, and the corresponding wave function is also normalizable for some particular orderings of the operators. The Hamilton can be also written in terms of two interacting harmonic oscillators. But, when the interaction is turned off, one of the harmonic oscillators has positive energy, while the other has negative energy. A remarkable feature is that orderings of the operators from a classical Hamilton to a quantum mechanical one play a fundamental role in order for the Wheeler–DeWitt equation to have nontrivial solutions. In addition, the space-time is well quantized, even when it is classically singular.

A scalar-tensor theory of gravity, containing an arbitrary coupling function $F(\varphi )$ and a general potential $V(\varphi )$, is considered in the context of a spatially flat Friedmann-Lemaître-Robertson-Walker model. The use of reparametrization invariance enables a particular lapse parametrization in which the minisuperspace metric completely specifies the dynamics of the system. A requirement of the existence of the maximal possible number of autonomous integrals of motion is imposed. This leads to a flat minisuperspace metric realized by a particular relation between the coupling function and the potential. The space of solutions is completely described in terms of the three autonomous integrals of motion constructed by the Killing fields of the minisupermetric and an additional rheonomous emanating from the homothetic field. The solutions contain the arbitrary function which remains after the imposition of the relation between $F(\varphi )$ and $V(\varphi )$. To exemplify the use of the general results, we select some particular cases and study their physical implications through an effective energy-momentum tensor, which turns out to be that of a perfect fluid.

A variation of the Affleck-Dine mechanism was proposed to generate the observed baryon asymmetry by Hertzberg and Karouby [Phys. Rev. D 89, 006523 (2014); Phys. Lett. B 737, 34 (2014)], in which the inflaton was assumed to be a complex scalar field with a weakly broken $U(1)$ symmetry, and the baryon asymmetry generation was easily unified with the stage of inflation and reheating. We adapt this mechanism to a general natural inflation scenario and compare the results with those in chaotic inflation models. We compute the net particle number obtained at the end of inflation and transform it into a net baryon number after reheatings. We observed that in our natural inflation model, the desired baryon-to-photon ratio can be achieved equally well as in chaotic models.

We describe what cosmology looks like in the context of the geometric theory of gravity based on a single scalar field. There are two distinct classes of cosmological solutions. An interesting feature is the possibility of having a bounce without invoking exotic equations of state for the cosmic fluid. We also discuss cosmological perturbation and present the basis of structure formation by gravitational instability in the framework of the geometric scalar gravity.

We study effects of inhomogeneities on distance measures in an exact relativistic Swiss-cheese model of the Universe, focusing on the distance modulus. The model has $\mathrm{\Lambda }\mathrm{CDM}$ background dynamics, and the “holes” are nonsymmetric structures described by the Szekeres metric. The Szekeres exact solution of Einstein’s equations, which is inhomogeneous and anisotropic, allows us to capture potentially relevant effects on light propagation due to nontrivial evolution of structures in an exact framework. Light beams traversing a single Szekeres structure in different ways can experience either magnification or demagnification, depending on the particular path. Consistent with expectations, we find a shift in the distance modulus $\mu$ to distant sources due to demagnification when the light beam travels primarily through the void regions of our model. Conversely, beams are magnified when they propagate mainly through the overdense regions of the structures, and we explore a small additional effect due to time evolution of the structures. We then study the probability distributions of $\mathrm{\Delta }\mu ={\mu }_{\mathrm{\Lambda }\text{CDM}}-{\mu }_{\mathrm{SC}}$ for sources at different redshifts in various Swiss-cheese constructions, where the light beams travel through a large number of randomly oriented Szekeres holes with random impact parameters. We find for $\mathrm{\Delta }\mu$ the dispersions $0.004\le {\sigma }_{\mathrm{\Delta }\mu }\le 0.008$ mag for sources with redshifts $1.0\le z\le 1.5$, which are smaller than the intrinsic dispersion of, for example, magnitudes of type Ia supernovae. The shapes of the distributions we obtain for our Swiss-cheese constructions are peculiar in the sense that they are not consistently skewed toward the demagnification side, as they are in analyses of lensing in cosmological simulations. Depending on the source redshift, the distributions for our models can be skewed to either the demagnification or the magnification side, reflecting a limitation of these constructions. This could be the result of requiring the continuity of Einstein’s equations throughout the overall spacetime patchwork, which imposes the condition that compensating overdense shells must accompany the underdense void regions in the holes. The possibility to explore other uses of these constructions that could circumvent this limitation and lead to different statistics remains open.

Despite the great progress of current cosmological measurements, the nature of the dominant component of the Universe, coined dark energy, is still an open question. Early dark energy is a possible candidate which may also alleviate some fine-tuning issues of the standard paradigm. Using the latest available cosmological data, we find that the 95% C.L. upper bound on the early dark energy density parameter is ${\mathrm{\Omega }}_{\mathrm{eDE}}<0.009$. On the other hand, the dark energy component may be a stressed and inhomogeneous fluid. If this is the case, the effective sound speed and the viscosity parameters are unconstrained by current data. Future omniscopelike 21 cm surveys, combined with present cosmic microwave background data, could be able to distinguish between standard quintessence scenarios from other possible models with $2\sigma$ significance, assuming a non-negligible early dark energy contribution. The precision achieved on the ${\mathrm{\Omega }}_{\mathrm{eDE}}$ parameter from these 21 cm probes could be below $\mathcal{O}(10\%)$.

Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of ray-tracing simulations with random realizations of spurious shear. This allows us to quantify the errors and biases of the triplet $({\mathrm{\Omega }}_m,w,{\sigma }_8)$ derived from the power spectrum (PS), as well as from three different sets of non-Gaussian statistics of the lensing convergence field: Minkowski functionals (MFs), low-order moments (LMs), and peak counts (PKs). Our main results are as follows: (i) We find an order of magnitude smaller biases from the PS than in previous work. (ii) The PS and LM yield biases much smaller than the morphological statistics (MF, PK). (iii) For strictly Gaussian spurious shear with integrated amplitude as low as its current estimate of ${\sigma }_{\text{sys}}^2\approx {10}^{-7}$, biases from the PS and LM would be unimportant even for a survey with the statistical power of Large Synoptic Survey Telescope. However, we find that for surveys larger than $\approx 100{\mathrm{deg}}^2$, non-Gaussianity in the noise (not included in our analysis) will likely be important and must be quantified to assess the biases. (iv) The morphological statistics (MF, PK) introduce important biases even for Gaussian noise, which must be corrected in large surveys. The biases are in different directions in $({\mathrm{\Omega }}_m,w,{\sigma }_8)$ parameter space, allowing self-calibration by combining multiple statistics. Our results warrant follow-up studies with more extensive lensing simulations and more accurate spurious shear estimates.

We study general implications of the IceCube observations in the energy range from ${10}^6\mathrm{GeV}$ to ${10}^{10}\mathrm{GeV}$ for the origin of extragalactic ultrahigh energy cosmic rays assuming that high energy neutrinos are generated by the photomeson production of protons in the extragalactic universe. The PeV-energy neutrino flux observed by IceCube gives strong bounds on the photomeson-production optical depth of protons in their sources and the intensity of the proton component of extragalactic cosmic rays. The neutrino flux implies that extragalactic cosmic-ray sources should have the optical depth greater than $\sim 0.01$ and contribute to more than a few percent of the observed bulk of cosmic rays at 10 PeV. If the spectrum of cosmic rays from these extragalactic sources extends well beyond 1 EeV, the neutrino flux indicates that extragalactic cosmic rays are dominant in the observed total cosmic-ray flux at 1 EeV and above, favoring the dip transition model of cosmic rays. The cosmic-ray sources are also required to be efficient neutrino emitters with the optical depth close to unity in this case. The highest energy cosmic-ray ($\sim {10}^{11}\mathrm{GeV}$) sources should not be strongly evolved with redshift to account for the IceCube observations, suggesting that any cosmic-ray radiation scenarios involving distant powerful astronomical objects with strong cosmological evolution are strongly disfavored. These considerations conclude that none of the known extragalactic astronomical objects can be simultaneously a source of both PeV and trans-EeV energy cosmic rays. We also discuss a possible effect of cosmic-ray propagation in magnetized intergalactic space to the connection between the observed total cosmic-ray flux and neutrino flux.

Diffuse $\gamma$-ray emission is the most prominent observable signature of celestial cosmic-ray interactions at high energies. While already being investigated at GeV energies over several decades, assessments of diffuse $\gamma$-ray emission at TeV energies remain sparse. After completion of the systematic survey of the inner Galaxy, the H.E.S.S. experiment is in a prime position to observe large-scale diffuse emission at TeV energies. Data of the H.E.S.S. Galactic Plane Survey are investigated in regions off known $\gamma$-ray sources. Corresponding $\gamma$-ray flux measurements were made over an extensive grid of celestial locations. Longitudinal and latitudinal profiles of the observed $\gamma$-ray fluxes show characteristic excess emission not attributable to known $\gamma$-ray sources. For the first time large-scale $\gamma$-ray emission along the Galactic plane using imaging atmospheric Cherenkov telescopes has been observed. While the background subtraction technique limits the ability to recover modest variation on the scale of the H.E.S.S. field of view or larger, which is characteristic of the inverse Compton scatter-induced Galactic diffuse emission, contributions of neutral pion decay as well as emission from unresolved $\gamma$-ray sources can be recovered in the observed signal to a large fraction. Calculations show that the minimum $\gamma$-ray emission from ${\pi }^0$ decay represents a significant contribution to the total signal. This detection is interpreted as a mix of diffuse Galactic $\gamma$-ray emission and unresolved sources.