Coupling of gravity to matter viaSO(3, 2) gauge fields

We consider gravity from the quantum field theory point of view and introduce a natural way of coupling gravity to matter by following the gauge principle for particle interactions. The energy-momentum tensor for the matter fields is shown to be conserved and follows as a consequence of the dynamics in a spontaneously brokenSO(3, 2) gauge theory of gravity. All known interactions are described by the gauge principle at the microscopic level.     

Geometrodynamics vs. connection dynamics

The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. We analyze the standard Einstein-Hilbert theory (in any spacetime dimension), the Palatini and Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual theories in 3+1 dimensions. We also couple varions matter fields to these theories and briefly describe a pure spin-connection formulation of 3+1 gravity. We derive the Euler-Lagrange equations of motion from an action principle and perform a Legendre transform to obtain a Hamiltonian formulation of each theory. Since constraints are present in all these theories, we construct constraint functions and analyze their Poisson bracket algebra. We demonstrate, whenever possible, equivalences between the theories.     

Accretion on high derivative asymptotically safe black holes

Asymptotically safe gravity is an effective approach to quantum gravity.It is important to differentiate modified gravity,which is inspired by asymptotically safe gravity.In this study,we examine particle dynamics near the improved version of a Schwarzschild black hole.We assume that in the context of an asymptotically safe gravity scenario,the ambient matter surrounding the black hole is of isothermal nature,and we investigate the spherical accretion of matter by deriving solutions at critical points.The analysis of various values of the state parameter for isothermal test fluids,viz.,k=1,1/2,1/3,1/4 show the possibility of accretion onto an asymptotically safe black hole.We formulate the accretion problem as Hamiltonian dynamical system and explain its phase flow in detail,which reveals interesting results in the asymptotically safe gravity theory.     

Conformal transformations in metric‐affine gravity and ghosts

Conformal transformations play a widespread role in gravity theories in regard to their cosmological and other implications. In the pure metric theory of gravity, conformal transformations change the frame to a new one wherein one obtains a conformal‐invariant scalar–tensor theory such that the scalar field, deriving from the conformal factor, is a ghost. In this work, conformal transformations and ghosts will be analyzed in the framework of the metric‐affine theory of gravity. Within this framework, metric and connection are independent variables, and, hence, transform independently under conformal transformations. It will be shown that, if affine connection is invariant under conformal transformations, then the scalar field of concern is a non‐ghost, non‐dynamical field. It is an auxiliary field at the classical level, and might develop a kinetic term at the quantum level. Alternatively, if connection transforms additively with a structure similar to yet more general than that of the Levi‐Civita connection, the resulting action describes the gravitational dynamics correctly, and, more importantly, the scalar field becomes a dynamical non‐ghost field. The equations of motion, for generic geometrical and matter‐sector variables, do not reduce connection to the Levi‐Civita connection, and, hence, independence of connection from metric is maintained. Therefore, metric‐affine gravity provides an arena in which ghosts arising from the conformal factor are avoided thanks to the independence of connection from the metric.     

3D quantum gravity and effective noncommutative quantum field theory

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.     

van der Waals-like transition in fluidized granular matter

A phase separation of fluidized granular matter is presented. Molecular dynamics simulations of a system of grains in two spatial dimensions, with a vibrating wall and without gravity, exhibit the appearance, coalescence, and disappearance of bubbles. By identifying the mechanism responsible for the phase separation, we show that the phenomenon is analogous to the spinodal decomposition of the gas-liquid transition of the van der Waals model. We have deduced a macroscopic model for the onset of phase separation which agrees quite well with molecular dynamics simulations.     

Lie-algebra expansions, Chern–Simons theories and the Einstein–Hilbert Lagrangian

Starting from gravity as a Chern–Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein–Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincaré group enlarged by an Abelian ideal. Although the resulting action naively looks like general relativity plus corrections due to matter sources, it is shown that the non-minimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein–Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss–Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions.     

Inertia and Gravity: a New Approach to Dynamical Theory in General Relativity

A new approach to gravitational field dynamics is proposed, as an alternative to the standard formulation of General Relativity. The spacetime metric tensor is split, into an externally fixed background geometry (inertia) and a local dynamical field (gravity); and a dynamical theory of matter and gravity in the inertial background is developed. The physical origin of inertia (Mach's Principle), and its observable properties, are discussed. The coordinate representations of inertia and gravity are found to have an internal gauge degree of freedom, due to the Equivalence Principle; the transformation properties of these fields, and the notion of covariant gauge conditions, are discussed. The dynamics of matter and gravitic fields is then investigated, using: (i) The group of motion of the inertial background, appearing as an externally fixed Lie symmetry in the matter and gravity action principles, which yields weakly conserved energy-momentum-like objects; and (ii) an internal symmetry gauge group, yielding strongly conserved “internal currents”. A fully covariant field-theoretical formalism is used, in which all quantities and operations are tensorial; the well-known difficulties of “coordinate effects” in the standard nontensorial formulation are thus avoided. The physical significance of various types of conservation laws is discussed; and a complete family of energy-momentum tensors of gravity, covariantly conserved together with the matter energy-momentum, is deduced from a tensorial action principle. Treating gravity as an independent dynamical interaction, on an equal footing with other (matter) interactions, we are then finally led to the conclusion that the gravitic energy-momentum of a system is fully determined by the matter energy-momentum; various physical implications of this are discussed in some detail.     

Time and a physical Hamiltonian for quantum gravity

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach.     

Fermions in three-dimensional spinfoam quantum gravity

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity coupled to spinors. The technique used is based on a finite expansion in inverse fermion masses leading to the computation of the vacuum to vacuum transition amplitude of the theory. The path integral is derived as a sum over closed fermionic loops wrapping around the spinfoam. The effects of quantum torsion are realised as a modification of the intertwining operators assigned to the edges of the two-complex, in accordance with loop quantum gravity. The creation of non-trivial curvature is modelled by a modification of the pure gravity vertex amplitudes. The appendix contains a review of the geometrical and algebraic structures underlying the classical coupling of fermions to three dimensional gravity.     

Non-minimal quintessence: Dynamics and coincidence problem

Brans–Dicke scalar–tensor theory provides a conformal coupling of the scalar field with gravity in Einstein’s frame. This model is equivalent to an interacting quintessence in which dark matter is coupled to dark energy. This provides a natural mechanism to alleviate the coincidence problem. We investigate the dynamics of this model and show that it leads to comparable dark energy and dark matter densities today.     

Comparing dark matter models,modified Newtonian dynamics and modified gravity in accounting for galaxy rotation curves

We compare six models(including the baryonic model,two dark matter models,two modified Newtonian dynamics models and one modified gravity model) in accounting for galaxy rotation curves.For the dark matter models,we assume NFW profile and core-modified profile for the dark halo,respectively.For the modified Newtonian dynamics models,we discuss Milgrom's MOND theory with two different interpolation functions,the standard and the simple interpolation functions.For the modified gravity,we focus on Moffat's MSTG theory.We fit these models to the observed rotation curves of 9 high-surface brightness and 9 low-surface brightness galaxies.We apply the Bayesian Information Criterion and the Akaike Information Criterion to test the goodness-of-fit of each model.It is found that none of the six models can fit all the galaxy rotation curves well.Two galaxies can be best fitted by the baryonic model without involving nonluminous dark matter.MOND can fit the largest number of galaxies,and only one galaxy can be best fitted by the MSTG model.Core-modified model fits about half the LSB galaxies well,but no HSB galaxies,while the NFW model fits only a small fraction of HSB galaxies but no LSB galaxies.This may imply that the oversimplified NFW and core-modified profiles cannot model the postulated dark matter haloes well.     

Making the Case for Conformal Gravity

We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever. With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by ’t Hooft in which a connection between conformal gravity and Einstein gravity has been found.     

Vacuum Stability in Kaluza-Klein Geometric Sigma Models

In Kaluza-Klein geometric sigma models, the scalar fields coupled to higher-dimensional gravity are pure gauge. The gauge fixed theory contains no matter fields, and can consistently be reduced to 4 dimensions, provided the internal space is chosen in the form of a group manifold. The effective 4-dimensional theory includes standard Einstein and Yang-Mills sectors, and is free of the classical cosmological constant problem. In this paper, the stability of the internal excitations is analyzed. It is shown that the initial Lagrangian can be modified to lead to a classically stable effective 4-dimensional theory, independently of the particular group used, and retaining all the basic features of the unmodified theory.     

Aspects of quadratic gravity

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure R² theory is indeed ghost free. Then we point out that for flat backgrounds the pure R² theory propagates only a scalar massless mode and no spin‐two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti‐de Sitter, or by changing the long‐distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string‐ or M‐theory. We demonstrate that string theory on non‐compact manifolds, like a line bundle over , may indeed lead to gravity dynamics determined by a higher curvature action.     

Observational Constraints on the Modified Gravity Model (MOG) Proposed by Moffat: Using the Magellanic System

A simple model for the dynamics of the Magellanic Stream (MS), in the framework of modified gravity models is investigated. We assume that the galaxy is made up of baryonic matter out of context of dark matter scenario. The model we used here is named Modified Gravity (MOG) proposed by Moffat (J. Cosmol. Astropart. Phys. 003, 2005). In order to examine the compatibility of the overall properties of the MS under the MOG theory, the observational radial velocity profile of the MS is compared with the numerical results using the χ ² fit method. In order to obtain the best model parameters, a maximum likelihood analysis is performed. We also compare the results of this model with the Cold Dark Matter (CDM) halo model and the other alternative gravity model that proposed by Bekenstein (Phys. Rev. D 70:083509, 2004), so called TeVeS. We show that by selecting the appropriate values for the free parameters, the MOG theory seems to be plausible to explain the dynamics of the MS as well as the CDM and the TeVeS models.     

Long-Wavelength Approximation for String Cosmology with Barotropic Perfect Fluid

The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded by the number of spatial gradients. In the zero order, a quasi-isotropic solution is presented and compared with the general solution of the pure dilaton gravity. Possible cosmological models are analyzed from the point of view of the pre-big bang scenario. The second order solutions are found and their growing and decaying parts are studied.     

The Role of Time in Relational Quantum Theories

We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical dynamics of the system and must therefore be deemed inappropriate. We propose a new strategy for consistently quantizing systems with a relational notion of time that does capture the full classical dynamics of the system and allows for evolution parametrized by an equitable internal clock. This proposal contains the minimal temporal structure necessary to retain the ordering of events required to describe classical evolution. In the context of shape dynamics (an equivalent formulation of general relativity that is locally scale invariant and free of the local problem of time) our proposal can be shown to constitute a natural methodology for describing dynamical evolution in quantum gravity and to lead to a quantum theory analogous to the Dirac quantization of unimodular gravity.     

Neutron stars in Scalar-Tensor-Vector Gravity

Scalar-Tensor-Vector Gravity (STVG), also referred as Modified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to describe Solar System observations, galaxy rotation curves, dynamics of clusters of galaxies, and cosmological data, without the imposition of dark components. The theory was formulated by John Moffat in 2006. In this work, we derive matter-sourced solutions of STVG and construct neutron star models. We aim at exploring STVG predictions about stellar structure in the strong gravity regime. Specifically, we represent spacetime with a static, spherically symmetric manifold, and model the stellar matter content with a perfect fluid energy-momentum tensor. We then derive the modified Tolman–Oppenheimer–Volkoff equation in STVG and integrate it for different equations of state. We find that STVG allows heavier neutron stars than General Relativity (GR). Maximum masses depend on a normalized parameter that quantifies the deviation from GR. The theory exhibits unusual predictions for extreme values of this parameter. We conclude that STVG admits suitable spherically symmetric solutions with matter sources, relevant for stellar structure. Since recent determinations of neutron stars masses violate some GR predictions, STVG appears as a viable candidate for a new gravity theory.