We study the SU(3) gluon propagator in renormalizable $R_{\xi }$ gauges implemented on a symmetric lattice with a total volume of $(3.25\mathrm{fm}{)}^4$ for values of the gauge fixing parameter up to $\xi =0.5$. As expected, the longitudinal gluon dressing function stays constant at its tree-level value $\xi$. Similar to the Landau gauge, the transverse $R_{\xi }$ gauge gluon propagator saturates at a nonvanishing value in the deep infrared for all values of $\xi$ studied.

Single- and double-heavy baryons are studied in the constituent quark model. The model Hamiltonian is chosen as a standard one with two exceptions: (1) the color-Coulomb term depends on quark masses and (2) an antisymmetric $LS$ (spin-orbit) force is introduced. Model parameters are fixed by the strange baryon spectra, $\mathrm{\Lambda }$ and $\mathrm{\Sigma }$ baryons. The masses of the observed charmed and bottomed baryons are, then, fairly well reproduced. Our focus is on the low-lying negative-parity states, in which the heavy baryons show specific excitation modes reflecting the mass differences of heavy and light quarks. By changing quark masses from the SU(3) limit to the strange quark mass, and, further, to the charm and bottom quark masses, we demonstrate that the spectra change from the SU(3) symmetry patterns to the heavy-quark-symmetry ones.

Naively applying holographic duality to gapped gravity on anti-de Sitter space seems to suggest that the stress tensor of the field theory dual cannot be conserved. On the other hand, by symmetry arguments, it seems that the dual should not violate Poincare symmetry. To clarify this apparent contradiction, we study a holographic dual of massive gravity where both the physical background metric and the fiducial metric are anti-de Sitter. Using the anomalous scaling of the energy-momentum tensor as our guide, we conclude that the dual theory is nonlocal. We find that the dual is similar to conformal invariant “unparticle” theories. We show that such theories can be viewed as dimensional reductions of flat-space field theories with inhomogeneous scaling properties.

We study the SU(2) Georgi-Glashow model and suggest a decomposition for its fields and obtain a Lagrangian based on new variables. We use Cho’s restricted decomposition as a result of a vacuum condition of the Georgi-Glashow model. This model with no external sources leads us to the Cho extended decomposition. We interpret the puzzling field, $\mathbf{n}$, in Cho’s decomposition as the color direction of the scalar field in the Georgi-Glashow model. We also study another constraint, condensate phase, and generalize Cho’s extended decomposition. Finally, we argue about a decomposition form that Faddeev and Niemi proposed in this constrained Georgi-Glashow model.

Violations of local Lorentz invariance in the gravitationally coupled matter sector have yet to be sought in strong-gravity systems. We present the implications of matter-sector Lorentz violation for orbital perturbations in pulsar systems and show that the analysis of pulsar data can provide sensitivities to these effects that exceed the current reach of Solar System and laboratory tests by several orders of magnitude.

We show how small neutrino rest masses can increase the expansion rate near the photon decoupling epoch in the early Universe, causing an earlier, higher temperature freeze-out for ionization equilibrium compared to the massless neutrino case. This yields a larger free-electron fraction, thereby affecting the photon diffusion length differently than the sound horizon at photon decoupling. This neutrino-mass and recombination effect depends strongly on the neutrino rest masses. Though below current sensitivity, this effect could be probed by next-generation cosmic microwave background experiments, giving another observational handle on neutrino rest mass.

We study the entanglement between two coupled detectors, the internal degrees of freedom of which are modeled by harmonic oscillators, interacting with a common quantum field, paying special attention to two less studied yet important features: finite separation and direct coupling. Distance dependence is essential in quantum teleportation and relativistic quantum information considerations. The presence of a quantum field as the environment accords an indirect interaction between the two oscillators at finite separation of a non-Markovian nature which competes with the direct coupling between them. The interplay between these two factors results in a rich variety of interesting entanglement behaviors at late times. We show that the entanglement behavior reported in prior work assuming no separation between the detectors can at best be a transient effect at very short times and claims that such behaviors represent late-time entanglement are misplaced. Entanglement between the detectors with direct coupling enters in the consideration of macroscopic quantum phenomena and other frontline issues. We find that with direct coupling entanglement between the two detectors can sustain over a finite distance, in contrast to the no direct coupling case reported before, where entanglement cannot survive at a separation more than a few inverse high-frequency cutoff scales. This work provides a functional platform for systematic investigations into the entanglement behavior of continuous variable quantum systems, such as used in quantum electro- and optomechanics.

In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition function into partial contributions associated with different sectors, containing center vortices and correlated monopoles. We show that, on each sector, the gauge fixed path integral displays a BRST symmetry. However, it cannot be globally extended due to sector-dependent boundary conditions on the ghost fields. These are nice features as they would permit us to discuss the independence of the partial contributions on gauge parameters, while opening a window for the space of quantum states to be different from the perturbative one, which would be implied if topological configurations were removed.

In a class of Gleyzes-Langlois-Piazza-Vernizzi theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $\varphi$ with respect to the radius $r$ vanish. If the parameter ${\alpha }_{\mathrm{H}}$ characterizing the deviation from Horndeski theories approaches a nonzero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2{\alpha }_{\mathrm{H}}/r^2$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The conical singularity can disappear for the models in which the parameter ${\alpha }_{\mathrm{H}}$ vanishes in the limit that $r\to 0$. We propose explicit models without the conical singularity by properly designing the classical Lagrangian in such a way that the main contribution to ${\alpha }_{\mathrm{H}}$ comes from the field derivative ${\varphi }^{\prime }(r)$ around $r=0$. We show that the extension of covariant Galileons with a diatonic coupling allows for the recovery of general relativistic behavior inside a so-called Vainshtein radius. In this case, both the propagation of a fifth force and the deviation from Horndeski theories are suppressed outside a compact body in such a way that the model is compatible with local gravity experiments inside the solar system.

The possibility to have singular accelerated evolution in the context of $F(R)$ bimetric gravity is investigated. Particularly, we study two singular models of cosmological evolution, one of which is a singular modified version of the Starobinsky $R^2$ inflation model. As we demonstrate, for both models in some cases, the slow-roll parameters become singular at the Type IV singularity, a fact that we interpret as a dynamical instability of the theory under study. This dynamical instability may be an indicator of a graceful exit from inflation, and we thoroughly discuss this scenario and the interpretation of the singular slow-roll parameters. Furthermore, it is demonstrated that for some versions of $F(R)$ bigravity, singular inflation is realized in a consistent way so that inflationary indices are compatible with Planck data. Moreover, we study the late-time behavior of the two singular models, and we show that the unified description of early- and late-time acceleration can be achieved in the context of bimetric $F(R)$ gravity.

We analytically compute, through the eight-and-a-half post-Newtonian order and the fourth-order in spin, the gravitational self-force correction to Detweiler’s gauge invariant redshift function for a small mass in circular orbit around a Kerr black hole. Using the first law of mechanics for black hole binaries with spin [L. Blanchet, A. Buonanno and A. Le Tiec, Phys. Rev. D 87, 024030 (2013)] we transcribe our results into a knowledge of various spin-dependent couplings, as encoded within the spinning effective-one-body model of T. Damour and A. Nagar [Phys. Rev. D 90, 044018 (2014)]. We also compare our analytical results to the (corrected) numerical self-force results of A. G. Shah, J. L. Friedman and T. S. Keidl [Phys. Rev. D 86, 084059 (2012)], from which we show how to directly extract physically relevant spin-dependent couplings.

The problem of obtaining a gauge independent beta function for Newton’s constant is addressed. By a specific parametrization of metric fluctuations a gauge independent functional integral is constructed for the semiclassical theory around an arbitrary Einstein space. The effective action then has the property that only physical polarizations of the graviton contribute, while all other modes cancel with the functional measure. We are then able to compute a gauge independent beta function for Newton’s constant in $d$ dimensions to one-loop order. No Landau pole is present provided $N_g<18$, where $N_g=d(d-3)/2$ is the number of polarizations of the graviton. While adding a large number of matter fields can change this picture, the absence of a pole persists for the particle content of the standard model in four spacetime dimensions.

In this paper we seek for relevant information on the asymptotic cosmological dynamics of the Brans-Dicke theory of gravity for several self-interaction potentials. By means of the simplest tools of the dynamical systems theory, it is shown that the general relativity de Sitter solution is an attractor of the Jordan frame (dilatonic) Brans-Dicke theory only for the exponential potential $U(\phi )\propto \exp \phi$, which corresponds to the quadratic potential $V(\varphi )\propto {\varphi }^2$ in terms of the original Brans-Dicke field $\varphi =\exp \phi$, or for potentials which approach to $\exp \phi$ at the stable point. At the de Sitter attractor, as well as at the stiff-matter equilibrium configurations, the dilaton is necessarily massless. We find bounds on the Brans-Dicke coupling constant ${\omega }_{\mathrm{BD}}$, which are consistent with well-known results.

We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific $\ell$-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order ($\sim t^{-2\ell -3}$), a new logarithmic behavior at third leading order ($\sim t^{-2\ell -5}\ln t$). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a “perturbative regime.”

In this paper, we construct a new class of black hole solutions which is coupled to the logarithmic nonlinear electrodynamics in the context of dilaton gravity. We consider an $n$-dimensional action in which gravity is coupled to the logarithmic nonlinear electrodynamics field and a scalar dilaton field to obtain the equations of motion of the gravitational, dilaton and electromagnetic fields. This leads to finding a new class of $n$-dimensional static and spherically symmetric black hole solutions in the presence of two Liouville-type dilaton potentials. The asymptotic behavior of these solutions is neither flat nor (anti-)de Sitter [(A)dS], and in the limiting case where the nonlinear parameter $\beta$ goes to infinity, our solutions reduce to the black holes of Einstein-Maxwell-dilaton gravity in higher dimensions. Thermodynamic quantities such as mass, temperature, electric potential and entropy are also computed, and it is shown that they agree with the first law of thermodynamics. Furthermore, we find that for small values of the electric charge parameter $q$, and the dilaton coupling constant $\alpha$, as well as small dimension $n$, the solutions are thermally stable. By increasing $n$, the region of stability stands for smaller values of $\alpha$ independent of $q$. Finally, we use the method of thermodynamical geometry and find the phase transition points by calculating the Ricci scalar of a thermodynamic metric.

For any vacuum initial data set, we define a local, non-negative scalar quantity that vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity depends only on the quantities used to construct the vacuum initial data set that are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor that plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the nonlinear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

Future cosmological measurements should enable the sum of neutrino masses to be determined indirectly through their effects on the expansion rate of the Universe and the clustering of matter. We consider prospects for the gravitationally lensed cosmic microwave background (CMB) anisotropies and baryon acoustic oscillations (BAOs) in the galaxy distribution, examining how the projected uncertainty of $\approx 15\mathrm{meV}$ on the neutrino mass sum (a $4\sigma$ detection of the minimal mass) might be reached over the next decade. The current $1\sigma$ uncertainty of $\approx 103\mathrm{meV}$ ($\text{Planck}\text{−}2015+\mathrm{BAO}\text{−}15$) will be improved by upcoming “Stage-3” (S3) CMB experiments ($\mathrm{S}3+\mathrm{BAO}\text{−}15:44\mathrm{meV}$), then upcoming BAO measurements ($\mathrm{S}3+\mathrm{DESI}:22\mathrm{meV}$), and planned next-generation “Stage 4” (S4) CMB experiments ($\mathrm{S}4+\mathrm{DESI}:15–19\mathrm{meV}$, depending on angular range). An improved optical depth measurement is important: the projected neutrino mass uncertainty increases to 26 meV if S4 is limited to $\ell >20$ and combined with current large-scale polarization data. Looking beyond $\mathrm{\Lambda }\mathrm{CDM}$, including curvature uncertainty increases the forecast mass error by $\approx 50\%$ for $\mathrm{S}4+\mathrm{DESI}$, and more than doubles the error with a two-parameter dark-energy equation of state. Complementary low-redshift probes including galaxy lensing will play a role in distinguishing between massive neutrinos and a departure from a $w=-1$, flat geometry.

We consider the case of very low reheating scenarios [$T_{\mathrm{RH}}\sim \mathcal{O}(\mathrm{MeV})$] with a better calculation of the production of the relic neutrino background (with three-flavor oscillations). At 95% confidence level, a lower bound on the reheating temperature $T_{\mathrm{RH}}>4.1\mathrm{MeV}$ is obtained from big bang nucleosynthesis, while $T_{\mathrm{RH}}>4.7\mathrm{MeV}$ from Planck data (allowing neutrino masses to vary), the most stringent bound on the reheating temperature to date. Neutrino masses as large as 1 eV are possible for very low reheating temperatures.

We study inflation with anisotropic hair induced by form fields. In four dimensions, the relevant form fields are gauge (one-form) fields and two-form fields. Assuming the exponential form of potential and gauge kinetic functions, we find new exact power-law solutions endowed with anisotropic hair. We also explore the phase space of anisotropic inflation and find fixed points corresponding to the exact power-law solutions. Moreover, we perform the stability analysis around the fixed points to reveal the structure of the phase space. It turns out that one of the fixed points becomes an attractor and others (if any) are saddle points. In particular, the one corresponding to anisotropic inflation becomes an attractor when it exists. We also argue that various anisotropic inflation models can be designed by choosing coupling constants.

We consider small perturbations about homogeneous backgrounds in dilatationally invariant Galileon models. The issues we address are stability (absence of ghosts and gradient instabilities) and superluminality. We show that in the Minkowski background, it is possible to construct the Lagrangian in such a way that any homogeneous Galileon background solution is stable and small perturbations about it are subluminal. On the other hand, in the case of Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds, for any Lagrangian functions there exist homogeneous background solutions to the Galileon equation of motion and time dependence of the scale factor, such that the stability conditions are satisfied, but the Galileon perturbations propagate with superluminal speed.