International Journal of Modern Physics D

Mindful of the anomalous perihelion precession of Mercury discovered by Le Verrier in the second half of the nineteenth century and its successful explanation by Einstein with his General Theory of Relativity in the early years of the twentieth century, discrepancies among observed effects in our Solar system and their theoretical predictions on the basis of the currently accepted laws of gravitation applied to known matter-energy distributions have the potential of paving the way for remarkable advances in fundamental physics. This is particularly important now more than ever, given that most of the universe seems to be made of unknown substances dubbed Dark Matter and Dark Energy. Should this not be directly the case, Solar system's anomalies could anyhow lead to advancements in either cumulative science, as shown to us by the discovery of Neptune in the first half of the nineteenth century, and technology itself. Moreover, investigations in one of such directions can serendipitously enrich the other one as well. The current status of some alleged gravitational anomalies in the Solar system is critically reviewed. They are: (a) Possible anomalous advances of planetary perihelia. (b) Unexplained orbital residuals of a recently discovered moon of Uranus (Mab). (c) The lingering unexplained secular increase of the eccentricity of the orbit of the Moon. (d) The so-called Faint Young Sun Paradox. (e) The secular decrease of the mass parameter of the Sun. (f) The Flyby Anomaly. (g) The Pioneer Anomaly. (h) The anomalous secular increase of the astronomical unit.

Possible violations of fundamental physical principles, e.g. the Einstein equivalence principle on which all metric theories of gravity are based, including general relativity (GR), would lead to a rotation of the plane of polarization for linearly polarized radiation traveling over cosmological distances, the so-called cosmic polarization rotation (CPR). We review here the astrophysical tests which have been carried out so far to check if CPR exists. These are using the radio and ultraviolet polarization of radio galaxies and the polarization of the cosmic microwave background (both E-mode and B-mode). These tests so far have been negative, leading to upper limits of the order of one degree on any CPR angle, thereby increasing our confidence in those physical principles, including GR. We also discuss future prospects in detecting CPR or improving the constraints on it.

We review a number of old and new concepts in quantum gauge theories, some of which are well-established but not widely appreciated, some are most recent, that may have analogs in gauge formulations of quantum gravity, loop quantum gravity, and their topological versions, and may be of general interest. Such concepts involve noncommutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual (ASD) variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse–Smale–Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-NSU(N) Yang–Mills (YM), that is reviewed as well.

Algebraic considerations furnish a measure of the mathematical complexity of a complete solution of large-NSU(N) YM: In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II₁ nonhyperfinite factor.

Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, since the interaction is subleading in , a vast simplification. It is an open problem, determined by the growth of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite.

Moreover, the sum of free propagators that occurs in the two-point correlators in the aforementioned local subalgebra must be asymptotic for large momentum to the result implied by the asymptotic freedom and the renormalization group: This fundamental constraint fixes asymptotically the residues of the poles of the propagators in terms of the mass spectrum and of the anomalous dimensions of the local operators.

For the mass gap problem, in the search of a hyperfinite subalgebra containing the scalar sector of large-N YM, a major role is played by the existence of a TFT underlying the large-N limit of YM, with twisted boundary conditions on a torus or, which is the same by Morita duality, on a noncommutative torus.

The TFT is trivial at the leading large-N order and localized on a set of critical points by means of a quantum version of Morse–Smale–Floer homology, that involves loop equations in the ASD variables.

A hyperfinite sector arises by fluctuations around the trivial TFT, in which the joint spectrum of scalar and pseudoscalar glueballs is linear in the square of the masses with degeneracy k = 1, 2,…, and the two-point correlator satisfies the aforementioned fundamental constraint arising by the asymptotic freedom and the renormalization group.

Pulsars are wonderful gravitational probes. Their tiny size and stellar mass give their rotation periods a stability comparable to that of atomic frequency standards. This is especially true of the rapidly rotating "millisecond pulsars" (MSPs). Many of these rapidly rotating pulsars are in orbit with another star, allowing pulsar timing to probe relativistic perturbations to the orbital motion. Pulsars have provided the most stringent tests of theories of relativistic gravitation, especially in the strong-field regime, and have shown that Einstein's general theory of relativity is an accurate description of the observed motions. Many other gravitational theories are effectively ruled out or at least severely constrained by these results. MSPs can also be used to form a "Pulsar Timing Array" (PTA). PTAs are Galactic-scale interferometers that have the potential to directly detect nanohertz gravitational waves from astrophysical sources. Orbiting super-massive black holes in the cores of distant galaxies are the sources most likely to be detectable. Although no evidence for gravitational waves has yet been found in PTA data sets, the latest limits are seriously constraining current ideas on galaxy and black-hole evolution in the early universe.

We consider holographic superconductors related to the Schwarzschild black hole in the low energy limit of Hořava–Lifshitz spacetime. The nonrelativistic electromagnetic and scalar fields are introduced to construct a holographic superconductor model in Hořava–Lifshitz gravity and the results show that the α₂ term plays an important role, modifying the conductivity curve line by means of an attenuation of the conductivity.

We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical N-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using an arbitrary energy–momentum tensor and assumed to possess any number of internal multipole moments. The solution of the gravitational field equations in any reference frame is presented as a sum of three terms: (i) The inertial flat spacetime in that frame, (ii) unperturbed solutions for each body in the system that is covariantly transformed to the coordinates of this frame and (iii) the gravitational interaction term. We use the harmonic gauge conditions that allow reconstruction of a significant part of the structure of the post-Galilean coordinate transformation functions relating global coordinates of the inertial reference frame to the local coordinates of the noninertial frame associated with a particular body. The remaining parts of these functions are determined from dynamical conditions, obtained by constructing the relativistic proper reference frame associated with a particular body. In this frame, the effect of external forces acting on the body is balanced by the fictitious frame-reaction force that is needed to keep the body at rest with respect to the frame, conserving its relativistic three-momentum. We find that this is sufficient to determine explicitly all the terms of the coordinate transformation. The same method is then used to develop the inverse transformations. The resulting post-Galilean coordinate transformations have an approximate group structure that extends the Poincaré group of global transformations to the case of accelerating observers in a gravitational field of N-body system. We present and discuss the structure of the metric tensors corresponding to the reference frames involved, the rules for transforming relativistic gravitational potentials, the coordinate transformations between frames and the resulting relativistic equations of motion.

In this paper, we consider third-order Lovelock–Maxwell gravity with additional (F_μν F^μν)² term as a nonlinearity correction of the Maxwell theory. We obtain black hole solutions with various horizon topologies (and various number of horizons) in which their asymptotical behavior can be flat or anti-de Sitter with an effective cosmological constant. We investigate the effects of Lovelock and electrodynamic corrections on properties of the solutions. Then, we restrict ourselves to asymptotically flat solutions and calculate the conserved and thermodynamic quantities. We check the first law of thermodynamics for these black hole solutions and calculate the heat capacity to analyze stability. Although higher dimensional black holes in Einstein gravity are unstable, here we look for suitable constraints on the black hole radius to find thermally stable black hole solutions.

We show how the flat spacetime Galileon field theories (FSGFT) in arbitrary dimensions can be obtained through a Born–Infeld (BI) type structure. This construction involves a brane metric and nonlinear combinations of derivatives of a scalar field. Our setup gives rise to some Galileon tensors and vectors useful for the variational analysis which are related to the momentum density of the probe Lovelock branes floating in a N-dimensional flat bulk. We find further that the Noether currents associated to these Galileon theories may be written in terms of such tensors.

In order to study constraints imposed on kinematics of the Crab pulsar's jet, we consider motion of particles along co-rotating field lines in the magnetosphere of the Crab pulsar. It is shown that particles following the co-rotating magnetic field lines may attain velocities close to observable values. In particular, we demonstrate that if the magnetic field lines are within the light cylinder (LC), the maximum value of the velocity component parallel to the rotation axis is limited by 0.5c. This result in the context of the X-ray observations performed by Chandra X-ray Observatory seems to be quite indicative and useful to estimate the density of field lines inside the jet. Considering the three-dimensional (3D) field lines crossing the LC, we found that for explaining the force-free regime of outflows the magnetic field lines must asymptotically tend to the Archimedes spiral configuration. It is also shown that the 3D case may explain the observed jet velocity for appropriately chosen parameters of magnetic field lines.

We study the classical dynamics of a particle in Snyder spacetime, adopting the formalism of constrained Hamiltonian systems introduced by Dirac. We show that the motion of a particle in a scalar potential is deformed with respect to special relativity by terms of order βE². A remarkable result is that in the relativistic Snyder model a consistent choice of the time variable must necessarily depend on the dynamics. This is a consequence of the nontrivial mixing between position and momentum coordinates intrinsic to the Snyder model.

Within the framework of Chern–Simons (CS) modified gravity, we studied dark energy models. The new agegraphic dark energy (NADE) model, entropy-corrected new agegraphic dark energy (ECNADE) model and NADE model with generalized uncertainty principle (GUP) are investigated. For these models, we studied the evolution of scale factor a, Hubble parameter H and deceleration parameter q. On meantime, we studied the state finder parameters s and r. These models show some similar behavior with modified Chaplygin gas model in some regions, while in other regions some similarity with phantom and quintessence dark energy is noticed.

Current and upcoming surveys will measure the cosmological parameters with an extremely high accuracy. The primary goal of these observations is to eliminate some of the currently viable cosmological models created to explain the late-time accelerated expansion (either real or only inferred). However, most of the statistical tests used in cosmology have a strong requirement: the use of a model to fit the data. Recently there has been an increased interest on finding tests that are model independent, i.e. to have a function that depends entirely on observed quantities and not on the model, see for instance [C. Clarkson, B. Bassett and T. H. C. Lu, Phys. Rev. Lett.101 (2008) 011301, arXiv:0712.3457 [astro-ph]]. In this paper, we present an alternative consistency check at the perturbative level for a homogeneous and isotropic Universe filled with a dark energy component. This test makes use of the growth of matter perturbations data and it is able to detect a deviation from the standard cosmological model, which could later be attributed to a clustering dark energy component, a tension in the data or a modification of gravity, within the framework of a Friedmann–Lemaître–Robertson–Walker (FLRW) universe.