Deconstruction of Gravity

We review how one can construct a deconstructed gravity by a transverse latticification of 5D General Relativity. The obtained theory is a multigravity theory, with link fields that are explicitly constructed out of the metric. We also discuss the spectrum of the theory at the level of the linearized theory.     

Geons and (4+1) Gravity

Gravitational-electromagnetic entities geons are singularity-free solutions of the Einstein-Maxwell equations. These structures in cylindrical symmetry are considered here through the noncompactified Kaluza-Klein theory which describes geometrically the gravitation field and its sources.     

Solution for static,spherically symmetric Lovelock gravity coupled with Yang–Mills hierarchy

The hierarchies of both Lovelock gravity and power-Yang–Mills field are combined through gravity in a single theory. In static, spherically symmetric ansatz exact particular integrals are obtained in all higher dimensions. The advantage of such hierarchies is the possibility of choosing coefficients, which are arbitrary otherwise, to cast solutions into tractable forms. To our knowledge the solutions constitute the most general spherically symmetric metrics that incorporate complexities both of Lovelock and Yang–Mills hierarchies within the common context. A large portion of our general class of solutions concerns and addresses to black holes for which specific examples are given. Thermodynamical behaviors of the system is briefly discussed in particular dimensions.     

Accelerating cosmology in modified gravity with scalar field

The modified gravity with 1/R term (R being the scalar curvature) and the Einstein-Hilbert term is studied by incorporating the phantom scalar field. A number of cosmological solutions are derived in the presence of the phantom field in the perfect fluid background. It is shown: the current inflation obtained in the modified gravity is affected by the existence of the phantom field.     

High-statistics study of the low-energy cosmic-muons angular distribution: Results from MICRO

Summary We present results from MICRO, a muon telescope with good angular resolution, which has collected more than 31·10⁶ cosmic muons. Upper limits are given for the flux coming from point sources and for the periodic component from Cygnus X3.     

Can the Pioneer Anomaly be of Gravitational Origin? A Phenomenological Answer

In order to satisfy the equivalence principle, any non-conventional mechanism proposed to gravitationally explain the Pioneer anomaly, in the form in which it is presently known from the so-far analyzed Pioneer 10/11 data, cannot leave out of consideration its impact on the motion of the planets of the Solar System as well, especially those orbiting in the regions in which the anomalous behavior of the Pioneer probes manifested itself. In this paper we, first, discuss the residuals of the right ascension α and declination δ of Uranus, Neptune and Pluto obtained by processing various data sets with different, well-established dynamical theories (JPL DE, IAA EPM, VSOP). Second, we use the latest determinations of the perihelion secular precessions of some planets in order to put on the test two gravitational mechanisms recently proposed to accommodate the Pioneer anomaly based on two models of modified gravity. Finally, we adopt the ranging data to Voyager 2 when it encountered Uranus and Neptune to perform a further, independent test of the hypothesis that a Pioneer-like acceleration can also affect the motion of the outer planets of the Solar System. The obtained answers are negative.      

Gravitational Potentials of Triaxial Ellipsoids in Weyl Gravity

We present analytic expressions for the gravitational potentials associated with triaxial ellipsoids, spheroids, spheres and disks in Weyl gravity. The gravitational potentials of these configurations in Newtonian gravity, i.e. the potentials derived by integration of the Poisson equation Green's function 1/|r – r| over the volume of the configuration, are well known in the literature. Herein we present the results of the integration of |r – r|, the Green's function associated with the fourth order Laplacian ⁴ of Weyl gravity, over the volume of the configuration to obtain the resulting gravitational potentials within this specific theory. As an application of our calculations, we solve analytically Euler's equations pertaining to incompressible rotating fluids to show that, as in the case of Newtonian gravity, homogeneous prolate configurations are not allowed within Weyl gravity either.     

Nordström's Theory Revisited

Maxwell–Nordström equations are rederived in the covariant form with respect to rotations in pseudo-orthogonal (4+1)-dimensional space, by the customary procedure of contraction of the excitation tensor and of the dual of the field tensor. For the invariance of these equations under time reversal T, the real fifth coordinate has to be odd with respect to the T-operation. Consequently, a new interpretation of the fifth coordinate is discussed, in which exp(it) is replaced by a function constructed from doubly-periodic Jacobian elliptic functions.     

A Proposal to Measure Antimatter Gravity Using Ultracold Antihydrogen Atoms

The gravitational acceleration of antimatter has never been measured directly. Antihydrogen atoms, being both stable and neutral, are an ideal system for investigating antimatter gravity. Ultralow temperatures in the 10–100 K range are desirable for practical experiments. It is proposed to cool positive antihydrogen ions using laser-cooled ordinary ions. Ultracold neutral antihydrogen atoms might then be obtained by photodetachment. The gravitational acceleration can readily be determined from the time-of-flight between the photodetachment laser pulse and an annihilation detector.     

Duality in Yang’s theory of gravity

The historical route and the current status of a curvature-squared model of gravity, in the affine form proposed by Yang, is briefly reviewed. Due to its inherent scale invariance, it enjoys some advantage for quantization, similarly as internal Yang-Mills fields. However, the exact vacuum solutions with double duality properties exhibit a vacuum degeneracy. By modifying the duality via a scale breaking term, we demonstrate that only the Einstein equations with induced cosmological constant emerge for the classical background, even when coupled to matter sources.     

Induced Gravity Theory from Noether Symmetry

We discuss the functional form of the potential and the non-minimal coupling in the scalar tensor gravity (induced gravity) theories as allowed by the Noether symmetry in the spatially homogenous and isotropic spacetime background. The solution of the field equations (for k=0) are presented by using the results obtained from the Noether symmetry. It has been observed that the potential and the coupling function obtained from the Noether symmetric approach do not satisfy the continuity equation for k=± 1. Finally we present an inflationary solution that goes over to the Einstein's gravity asymptotically as t .     

Cosmological tests of gravity

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher-dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories.The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ∼ kpc (galaxy scales) to ∼ Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages — we summarize these tests and discuss the interesting prospects for new tests in the coming decade.     

Proof of a universal lower bound on the shear viscosity to entropy density ratio

It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/4π$1/4\pi$ in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.     

Exact solution to the “auxiliary extra-dimension” model of massive gravity

The “auxiliary extra-dimension” model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.     

Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity

We analyze locally anisotropic configurations modeled by anholonomic frames with associated nonlinear connections in general relativity, affine–Poincarè and/or de Sitter gauge gravity and Kaluza–Klein theories. A suitable geometrical formalism for theories with higher order anisotropies and non compactified extra dimensions is introduced. We give a mostly self–containing review of some aspects of gauge models of gravity and discuss their anholonomic generalizations and the conditions of equivalence with the Einstein gravity in arbitrary dimensions. New classes of cosmological solutions describing Friedmann–Robertson–Walker like universes with resolution ellipsoid or torus symmetry.     

Some Properties of Multigravity Theories and Discretized Brane Worlds

We review some properties of solutions to 5D Einstein gravity with a discrete fifth dimension. Those properties depend on the discretization scheme we use. In particular, we find that the neglect of the lapse field (along the discretized direction) gives rise to Randall–Sundrum-type metric with a negative tension brane. However, no brane source is required. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We show also that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales.     

Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

We review and extend in several directions recent results on the “asymptotic safety” approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian renormalization group equation. We begin by discussing various cutoff schemes, i.e. ways of implementing the Wilsonian cutoff procedure. We compare the beta functions of the gravitational couplings obtained with different schemes, studying first the contribution of matter fields and then the so-called Einstein-Hilbert truncation, where only the cosmological constant and Newton’s constant are retained. In this context we make connection with old results, in particular we reproduce the results of the epsilon expansion and the perturbative one-loop divergences. We then apply the Renormalization Group to higher derivative gravity. In the case of a general action quadratic in curvature we recover, within certain approximations, the known asymptotic freedom of the four-derivative terms, while Newton’s constant and of the cosmological constant have a nontrivial fixed point. In the case of actions that are polynomials in the scalar curvature of degree up to eight we find that the theory has a fixed point with three UV-attractive directions, so that the requirement of having a continuum limit constrains the couplings to lie in a three-dimensional subspace, whose equation is explicitly given. We emphasize throughout the difference between scheme-dependent and scheme-independent results, and provide several examples of the fact that only dimensionless couplings can have “universal” behavior.