In order to extract continuum properties, we study the topological charge density correlator (TCDC) and the inverse participation ratio (IPR) for the topological charge density $q(x)$ in SU(3) lattice Yang-Mills theory for relatively small lattice spacings, including some smaller than those explored before. With the help of a recently proposed open boundary condition, it is possible to compute observables at a smaller lattice spacing since the trapping problem is absent. On the other hand, the reference energy scale provided by the Wilson flow allows us to study their scaling behavior, in contrast to previously proposed smearing techniques. The behavior of the TCDC for different lattice spacings at a fixed hypercubic smearing level shows apparent scaling violations. In contrast, at a particular Wilson flow time $t$ for all of the lattice spacings investigated (except the largest one), the TCDC data show universal behavior within our statistical uncertainties. The continuum properties of the TCDC are studied by investigating the small-flow-time behavior. We also extract the pseudoscalar glueball mass from the TCDC, which appears to be insensitive to the lattice spacings ($0.0345\mathrm{fm}\le a\le 0.0667\mathrm{fm}$) and agrees with the value extracted using anisotropic lattices, within statistical errors. Further, we study the localization property of $q(x)$ using the IPR (whose continuum behavior can be probed using small values of the Wilson flow time) and observe a decrease of the IPR with decreasing Wilson flow time. A detailed study of $q(x)$ under the Wilson flow time reveals that as the Wilson flow time decreases, the proximity of the regions of positive and negative charge densities of large magnitude increases, and the charge density appears to be more delocalized, resulting in the observed behavior of the IPR.

We present the first numerical solution to the next-to-leading-order Balitsky-Kovchegov equation in coordinate space in the large-$N_{\mathrm{c}}$ limit. In addition to the dipole operator, we also solve the evolution of the “conformal dipole” for which the conformal invariance breaking double logarithmic term is absent from the evolution equation. The next-to-leading-order corrections are shown to slow down the evolution. We show that the solution depends strongly on the details of the initial condition and that the solution to the equation is not positive definite with all initial conditions relevant for phenomenological applications.

We analyze the conditions under which a statistical error analysis can be carried out in the case of $\pi \pi$ scattering, namely the normality of residuals in the conventional ${\chi }^2$-fit method. Here we check that the current and benchmarking analyses only present very small violations of the normality requirements. In particular, we show how it is possible to slightly amend the selection of the experimental data, and improve the normality of residuals. As an example, we discuss the $0^{++}$ channel and the implications for the $f_0(500)$ and $f_0(980)$ resonances, finding that the new selection of data provides very similar and compatible results. In addition, the effect on the $f_0(500)$ and $f_0(980)$ resonance pole parameters is almost negligible, which reinforces the central results and the uncertainty analysis performed in these benchmarking determinations.

We compute fragmentation functions for a quark to fragment to a quarkonium through an $S$-wave spin-triplet heavy quark-antiquark pair. We consider both color-singlet and color-octet heavy quark-antiquark ($Q\overline{Q}$) pairs. We give results for the case in which the fragmenting quark and the quark that is a constituent of the quarkonium have different flavors and for the case in which these quarks have the same flavors. Our results for the sum over all spin polarizations of the $Q\overline{Q}$ pairs confirm previous results. Our results for longitudinally polarized $Q\overline{Q}$ pairs agree with previous calculations for the same flavor cases and correct an error in a previous calculation for the different-flavor case.

The simplest neutrino mass models based on $A_4$ symmetry predict ${\theta }_{13}=0$ at tree level, a value that contradicts recent data. We study models that arise from the spontaneous breaking of an SO(3) symmetry to its $A_4$ subgroup, and find that such models can naturally accommodate a nonzero ${\theta }_{13}$ at tree level. Standard Model charged leptons mix with additional heavy ones to generate a ${\theta }_{13}$ that scales with the ratio of the $A_4$-breaking to SO(3)-breaking scales. A suitable choice of energy scales hence allows one to reproduce the correct lepton mixing angles. We also consider an alternative approach where we modify the alignment of flavons associated with the charged lepton masses, and find that the effects on ${\theta }_{13}$ are enhanced by a factor that scales as $m_{\tau }/m_{\mu }$.

The standard three-neutrino oscillation paradigm, associated with small squared mass splittings $\mathrm{\Delta }{m}^2\ll 0.1{\mathrm{eV}}^2$, has been successfully built up over the last 15 years using solar, atmospheric, long baseline accelerator and reactor neutrino experiments. However, this well-established picture might suffer from anomalous results reported at very short baselines in some of these experiments. If not experimental artifacts, such results could possibly be interpreted as the existence of at least an additional fourth sterile neutrino species, mixing with the known active flavors with an associated mass splitting $\mathrm{\Delta }{m}_{\text{new}}^2\gg 0.01{\mathrm{eV}}^2$ and being insensitive to standard weak interactions. Precision measurements at very short baselines (5–15 m) with intense MeV ${\overline{\nu }}_e$ emitters can be used to probe these anomalies. In this article, the expected ${\overline{\nu }}_e$ signal and backgrounds of a generic experiment which consists of deploying an intense ${\beta }^{-}$ radioactive source inside or in the vicinity of a large liquid scintillator detector are studied. The technical challenges to perform such an experiment are identified, along with quantifying the possible source- and detector-induced systematics and their impact on the sensitivity to the observation of neutrino oscillations at short baselines.

The dynamics of string fluctuations under a rotating Bañados-Teitelboim-Zanelli black hole is studied using the method developed in Son and Teaney [J. High Energy Phys. 07 (2009) 021]. We compare our result with the one computed previously in Atmaja [J. High Energy Phys. 02 (2013) 021], using a different method as developed in de Boer et al. [J. High Energy Phys. 07 (2009) 094] for the case of a corotating string. The result supports the claim made in Atmaja [J. High Energy Phys. 02 (2013) 021] that the end of the string, which is identified as an external quark at the boundary, behaves as a Brownian particle with the mass is given by an effective mass parameter $M_{\text{eff}}$ equals to the zero-temperature mass of an external quark $M_0$ times the cube of a Lorentz factor $\gamma$. Furthermore, we extend the computation to a higher dimensional rotating AdS black hole, where the metric is effectively asymptotic to ${\mathrm{AdS}}_3$ and the fluctuation is taken only along the corotating motion. It turns out that the effective mass of the external quark has a universal form of $M_{\text{eff}}={\gamma }^3{M}_0$.

In this article, we study the time-dependent Aharonov-Bohm effect for non-Abelian gauge fields. We use two well-known time-dependent solutions to the Yang-Mills field equations to investigate the Aharonov-Bohm phase shift. For both of the solutions, we find a cancellation between the phase shift coming from the non-Abelian “magnetic” field and the phase shift coming from the non-Abelian “electric” field, which inevitably arises in time-dependent cases. We compare and contrast this cancellation for the time-dependent non-Abelian case to a similar cancellation which occurs in the time-dependent Abelian case. We postulate that this cancellation occurs generally in time-dependent situations for both Abelian and non-Abelian fields.

We analyze the possible effects arising from the Planck scale regime upon the interference pattern of two noninteracting Bose-Einstein condensates. We start with the analysis of the free expansion of a condensate, and have taken into account the effects produced by a deformed dispersion relation, suggested in several quantum-gravity models. The analysis of the condensate free expansion, in particular, the modified free velocity expansion, suggests in a natural way, a modified uncertainty principle that could lead to new phenomenological implications related to the quantum structure of space-time. Finally, we analyze the corresponding separation between the interference fringes after the two condensates overlap, in order to explore the sensitivity of the system to possible signals caused by the Planck scale regime.

$f(R)$ theories of gravity are one of the most popular alternative explanations for dark energy, and therefore studying the possible astrophysical implications of these theories is an important task. In the present paper we make a substantial advance in this direction by considering rapidly rotating neutron stars in $R^2$ gravity. The results are obtained numerically, and the method we use is nonperturbative and self-consistent. The neutron star properties, such as mass, radius, and moment of inertia, are studied in detail. The results show that rotation magnifies the deviations from general relativity, and the maximum mass and moment of inertia can reach very high values. This observation is similar to the previous studies of rapidly rotating neutron stars in other alternative theories of gravity, such as scalar-tensor theories, and it can potentially lead to strong astrophysical manifestations.

The aim of this paper is to clarify the distinction between homoclinic and standard (global) Bondi-type accretion solutions in the Schwarzschild–anti–de Sitter space-time. The homoclinic solutions have recently been discovered numerically for polytropic equations of state. Here I show that they exist also for certain isothermal (linear) equations of state, and an analytic solution of this type is obtained. It is argued that the existence of such solutions is generic, although for sufficiently relativistic matter models (photon gas, ultrahard equation of state) there exist global solutions that can be continued to infinity, similarly to standard Michel’s solutions in the Schwarzschild space-time. In contrast to that global solutions should not exist for matter models with a nonvanishing rest-mass component, and this is demonstrated for polytropes. For homoclinic isothermal solutions I derive an upper bound on the mass of the black hole for which stationary transonic accretion is allowed.

In recent work [L. Blanchet and J. Novak, Mon. Not. R. Astron. Soc. 412, 2530 (2011); L. Blanchet and J. Novak, Testing MOND in the Solar System (2011); and M. Milgrom, Mon. Not. R. Astron. Soc. 399, 474 (2009)], the authors showed that modified Newton dynamics (MOND) has a non-negligible secular perturbation effect on planets with large semimajor axes (gaseous planets) in the Solar System. Some comets also have a very eccentric orbit with a large semimajor axis (Halley family comets) going far away from the Sun (more than 15 AU) in a low acceleration regime where they would be subject to MOND perturbation. They also approach the Sun very closely (less than 3 AU) and are affected by the sublimation of ices from their nucleus, triggering so-called nongravitational forces. The main goal of this paper is to investigate the effect of MOND perturbation on three comets with various orbital elements ($2\mathrm{P}/\text{Encke}$, $1\mathrm{P}/\text{Halley}$ and $153\mathrm{P}/\text{Ikeya}\text{−}\text{Zhang}$) and then compare it to the nongravitational perturbations. It is motivated by the fact that when fitting an outgassing model for a comet, we have to take into account all of the small perturbing effects to avoid absorbing these effects into the nongravitational parameters. Otherwise, we could derive a completely wrong estimation of the outgassing. For this work, we use six different forms of MOND functions and compute the secular variations of the orbital elements due to MOND and nongravitational perturbations. We show that, for comets with large semimajor axis, the MONDian effects are not negligible compared to the nongravitational perturbations.

An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the worldline of the body are essential tools to investigate both geometrical and physical properties of the tidal interaction. For example, one can determine the tidal potential in the neighborhood of the body by constructing a body-fixed frame, which requires Fermi-type coordinates attached to the body itself, the latter being in turn related to the spacetime metric and curvature along the considered worldline. Similarly, in an effective field theory description of extended bodies, finite size effects are taken into account by adding to the point mass action certain nonminimal couplings which involve integrals of tidal invariants along the orbit of the body. In both cases such a computation of tidal tensors is required. Here we consider the case of a spinning body also endowed with a nonvanishing quadrupole moment in a Kerr spacetime. The structure of the body is modeled by a multipolar expansion around the “center-of-mass line” according to the Mathisson-Papapetrou-Dixon model truncated at the quadrupolar order. The quadrupole tensor is assumed to be quadratic in spin, accounting for rotational deformations. The behavior of tidal invariants of both electric and magnetic type is discussed in terms of gauge-invariant quantities when the body is moving along a circular orbit as well as in the case of an arbitrary (equatorial) motion. The analysis is completed by examining the associated eigenvalues and eigenvectors of the tidal tensors. The limiting situation of the Schwarzschild solution is also explored both in the strong field regime and in the weak field limit.

Advanced LIGO may be the first experiment to detect gravitational waves. Through superradiance of stellar black holes, it may also be the first experiment to discover the QCD axion with decay constant above the grand unification scale. When an axion’s Compton wavelength is comparable to the size of a black hole, the axion binds to the black hole, forming a “gravitational atom.” Through the superradiance process, the number of axions occupying the bound levels grows exponentially, extracting energy and angular momentum from the black hole. Axions transitioning between levels of the gravitational atom and axions annihilating to gravitons can produce observable gravitational wave signals. The signals are long lasting, monochromatic, and can be distinguished from ordinary astrophysical sources. We estimate up to $\mathcal{O}(1)$ transition events at aLIGO for an axion between $10^{-11}$ and $10^{-10}\mathrm{eV}$ and up to $10^4$ annihilation events for an axion between $10^{-13}$ and $10^{-11}\mathrm{eV}$. In the event of a null search, aLIGO can constrain the axion mass for a range of rapidly spinning black hole formation rates. Axion annihilations are also promising for much lighter masses at future lower-frequency gravitational wave observatories; the rates have large uncertainties, dominated by supermassive black hole spin distributions. Our projections for aLIGO are robust against perturbations from the black hole environment and account for our updated exclusion on the QCD axion of $6\times 10^{-13}\mathrm{eV}<{\mu }_a<2\times 10^{-11}\mathrm{eV}$ suggested by stellar black hole spin measurements.

Strong lensing time delay cosmography has excellent complementarity with other dark energy probes and will soon have abundant systems detected. We investigate two issues in the imaging and spectroscopic follow-up required to obtain the time delay distance. The first is optimization of spectroscopic resources. We develop a code to optimize the cosmological leverage under the constraint of constant spectroscopic time and find that sculpting the lens system redshift distribution can deliver a 40% improvement in dark energy figure of merit. The second is the role of systematics, correlated between different quantities of a given system or model errors common to all systems. We show how the levels of different systematics affect the cosmological parameter estimation and derive guidance for the fraction of double image vs quad image systems to follow as a function of differing systematics between them.

Scalar field theories that possess a Vainshtein mechanism are able to dynamically suppress the associated fifth forces in the presence of massive sources through derivative nonlinearities. The resulting equations of motion for the scalar are highly nonlinear, and therefore very few analytic solutions are known. Here, we present a brief investigation of the structure of Vainshtein screening in symmetrical configurations, focusing in particular on the spherical, cylindrical and planar solutions that are relevant for observations of the cosmic web. We consider Vainshtein screening in both the Galileon model, where the nonlinear terms involve second derivatives of the scalar, and a $k$-essence theory, where the nonlinear terms involve only first derivatives of the scalar. We find that screening, and consequently the suppression of the scalar force, is most efficient around spherical sources, weaker around cylindrical sources and can be absent altogether around planar sources.

We describe a method using the integrated Sachs-Wolfe (ISW) effect caused by individual inhomogeneities to determine the cosmological parameters $H_0$, ${\mathrm{\Omega }}_{\mathrm{m}}$, and ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$, etc. This ISW-redshift test requires detailed knowledge of the internal kinematics of a set of individual density perturbations, e.g., galaxy clusters and/or cosmic voids, in particular their density and velocity profiles, and their mass accretion rates. It assumes the density perturbations are isolated and embedded (equivalently compensated) and makes use of the newly found relation between the ISW temperature perturbation of the cosmic microwave background (CMB) and the Fermat potential of the lens. Given measurements of the amplitudes of the temperature variations in the CMB caused by such clusters or voids at various redshifts and estimates of their angular sizes or masses, one can constrain the cosmological parameters. More realistically, the converse is more likely, i.e., if the background cosmology is sufficiently constrained, measurement of ISW profiles of clusters and voids (e.g., hot and cold spots and rings) can constrain dynamical properties of the dark matter, including accretion, associated with such lenses and thus constrain the evolution of these objects with redshift.

The propagation of TeV gamma rays can be strongly modified by $B$-field induced conversion to axionlike particles (ALPs). We show that, at such high energies, photon dispersion is dominated by background photons—the only example where photon-photon dispersion is of practical relevance. We determine the refractive index for all energies and find that, for fixed energy density, background photons below the pair-production threshold dominate. The cosmic microwave background alone provides an “effective photon mass” of $m_{\gamma }^2=-(1.01\mathrm{neV}\times \omega /\mathrm{TeV}{)}^2$ for $\omega \lesssim 1000\mathrm{TeV}$. The extragalactic background light is subdominant, but local radiation fields in the Galaxy or the source regions provide significant contributions. Photon-photon dispersion is small enough to leave typical scenarios of photon-ALP oscillations unscathed, but big enough to worry about it case by case.

We propose a quantum symmetry reduction of loop quantum gravity to Bianchi I spacetimes. To this end, we choose the diagonal metric gauge for the spatial diffeomorphism constraint at the classical level, leading to an ${\mathbb{R}}_{\text{Bohr}}$ gauge theory, and quantize the resulting theory via loop quantum gravity methods. Constraints which lead classically to a suitable reduction are imposed at the quantum level. The dynamics of the resulting model turn out to be very simple and manifestly coincide with those of a polymer quantization of a Bianchi I model for the simplest choice of full theory quantum states compatible with the Bianchi I reduction. In particular, the “improved” $\overline{\mu }$ dynamics of loop quantum cosmology can be obtained by modifying the regularization of the Hamiltonian constraint with similar ideas, in turn yielding insights into the full theory dynamics.