Generalization of Weyl's Unified Theory to Encompass a Non-Abelian Internal Symmetry Group
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Blaha, S.↗
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Compactly supported linearised observables in single-field inflation
We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) local gauge-invariant observables such as the linearised Weyl tensor, which have better infrared properties than the graviton and inflaton fields. Special cases include the equivalence between the compactly supported gauge-invariant graviton observable and the smeared linearised Weyl tensor in Minkowski and de Sitter spaces. Our results indicate that the infrared divergences in the tensor and scalar perturbations in single-field inflation have the same status as in de Sitter space and are both a gauge artefact, in a certain technical sense, at tree level.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Weyl relativity: a novel approach to Weyl's ideas
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the conformal invariance of the gravitational field. We highlight that changing the local symmetry group of spacetime permits to construct a theory in which these two symmetries are combined into a putative gauge symmetry but with second-order field equations and non-trivial mass scales, unlike the original higher-order construction by Weyl. We prove that the gravitational field equations are equivalent to the (trace-free) Einstein field equations, ensuring their compatibility with known tests of general relativity. As a corollary, the effective cosmological constant is rendered radiatively stable due to Weyl invariance. A novel phenomenological consequence characteristic of this construction, potentially relevant for cosmological observations, is the existence of an energy scale below which effects associated with the non-integrability of spacetime distances, and an effective mass for the electromagnetic field, appear simultaneously (as dual manifestations of the use of Weyl connections). We explain how former criticisms against Weyl's ideas lose most of their power in its present reincarnation, which we refer to as Weyl relativity, as it represents a Weyl-invariant, unified description of both the Einstein and Maxwell field equations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Primordial massive gravitational waves from Einstein-Chern-Simons-Weyl gravity
We investigate the evolution of cosmological perturbations during de Sitter inflation in the Einstein-Chern-Simons-Weyl gravity. Primordial massive gravitational waves are composed of one scalar, two vector and four tensor circularly polarized modes. We show that the vector power spectrum decays quickly like a transversely massive vector in the superhorizon limit z → 0. In this limit, the power spectrum coming from massive tensor modes decays quickly, leading to the conventional tensor power spectrum. Also, we find that in the limit of m{sup 2} → 0 (keeping the Weyl-squared term only), the vector and tensor power spectra disappear. It implies that their power spectra are not gravitationally produced because they (vector and tensor) are decoupled from the expanding de Sitter background, as a result of conformal invariance.
79 ASTRONOMY AND ASTROPHYSICS↗
Asymptotically Lifshitz brane-world black holes
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: Black-Right-Pointing-Pointer Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. Black-Right-Pointing-Pointer Studying the thermodynamical behavior of asymptotically Lifshitz black holes. Black-Right-Pointing-Pointer Showing that the entropy imposes the critical exponent z to be bounded from above. Black-Right-Pointing-Pointer Discussing the phase transition for different spatial topologies.
79 ASTRONOMY AND ASTROPHYSICS↗
Some cosmological consequences of Weyl invariance
We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of N conformally coupled scalar fields. It will be shown that when the FRW ansatz for the spacetime metric is assumed, the Ward identity for conformal invariance guarantees that the gravitational equations hold whenever the scalar fields EM do so. It follows that any scale factor can solve the theory provided a non-trivial profile for a dilaton field. In particular, accelerated expansion is a natural solution to the full set of equations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Cosmology for quadratic gravity in generalized Weyl geometry
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity
We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the 'usual' hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by 'the particle creation law', proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel'dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the 'empty vacuum', there may exist the 'dynamical vacuum', which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The weight of matter
Einstein's traceless 1919 gravitational theory is analyzed from a variational viewpoint. It is shown to be equivalent to a transverse (invariant only under diffeomorphisms that preserve the Lebesgue measure) theory, with an additional Weyl symmetry, in which the gauge is partially fixed so that the metric becomes unimodular. In spite of the fact that this symmetry forbids direct coupling of the potential energy with the gravitational sector, the equivalence principle is recovered in the unimodular gauge owing to Bianchi's identities.
79 ASTRONOMY AND ASTROPHYSICS↗
The Weyl tensor correlator in cosmological spacetimes
We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ϵ and δ, and the result is shown to have the correct de Sitter limit as ϵ,δ→0. Furthermore, it is seen that the Weyl tensor correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Galilean conformal and superconformal symmetries
Firstly we discuss briefly three different algebras named as nonrelativistic (NR) conformal: Schroedinger, Galilean conformal, and infinite algebra of local NR conformal isometries. Further we shall consider in some detail Galilean conformal algebra (GCA) obtained in the limit c{yields}{infinity} from relativistic conformal algebraO(d+1, 2) (d-number of space dimensions). Two different contraction limits providing GCA and some recently considered realizations will be briefly discussed. Finally by considering NR contraction of D = 4 superconformal algebra the Galilei conformal superalgebra (GCSA) is obtained, in the formulation using complexWeyl supercharges.
74 ATOMIC AND MOLECULAR PHYSICS↗
On the null trajectories in conformal Weyl gravity
In this work we find analytical solutions to the null geodesics around a black hole in the conformal Weyl gravity. Exact expressions for the horizons are found, and they depend on the cosmological constant and the coupling constants of the conformal Weyl gravity. Then, we study the radial motion from the point of view of the proper and coordinate frames, and compare it with that found in spacetimes of general relativity. The angular motion is also examined qualitatively by means of an effective potential; quantitatively, the equation of motion is solved in terms of wp-Weierstrass elliptic function. Thus, we find the deflection angle for photons without using any approximation, which is a novel result for this kind of gravity.
79 ASTRONOMY AND ASTROPHYSICS↗
Spherically symmetric conformal gravity and ''gravitational bubbles''
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
79 ASTRONOMY AND ASTROPHYSICS↗
Constraint on dark matter central density in the Eddington inspired Born-Infeld (EiBI) gravity with input from Weyl gravity
Recently, Harko et al. (2014) derived an approximate metric of the galactic halo in the Eddington inspired Born-Infeld (EiBI) gravity. In this metric, we show that there is an upper limit ρ {sub 0}{sup upper} on the central density ρ {sub 0} of dark matter such that stable circular orbits are possible only when the constraint ρ {sub 0}≤ ρ {sub 0}{sup upper} is satisfied in each galactic sample. To quantify different ρ {sub 0}{sup upper} for different samples, we follow the novel approach of Edery and Paranjape (1998), where we use as input the geometric halo radius R{sub WR} from Weyl gravity and equate it with the dark matter radius R{sub DM} from EiBI gravity for the same halo boundary. This input then shows that the known fitted values of ρ {sub 0} obey the constraint ρ {sub 0}≤ ρ {sub 0}{sup upper}∝ (R{sub WR}){sup −2}. Using the mass-to-light ratios giving α , we shall also evaluate ρ {sub 0}{sup lower} ∝ (α −1)M{sub lum}R{sub WR}{sup −3} and the average dark matter density ( ρ ) {sup lower}. Quantitatively, it turns out that the interval ρ {sub 0}{sup lower} ≤ ρ {sub 0}≤ ρ {sub 0}{sup upper} verifies reasonably well against many dark matter dominated low surface brightness (LSB) galaxies for which values of ρ {sub 0} are independently known. The interval holds also in the case of Milky Way galaxy. Qualitatively, the existence of a stability induced upper limit ρ {sub 0}{sup upper} is a remarkable prediction of the EiBI theory.
79 ASTRONOMY AND ASTROPHYSICS↗
Weyl gravity revisited
The on shell equivalence of first order and second order formalisms for the Einstein-Hilbert action does not hold for those actions quadratic in curvature. It would seem that by considering the connection and the metric as independent dynamical variables, there are no quartic propagators for any dynamical variable. This suggests that it is possible to get both renormalizability and unitarity along these lines. We have studied a particular instance of those theories, namely Weyl gravity. In this first paper we show that it is not possible to implement this program with the Weyl connection alone.
79 ASTRONOMY AND ASTROPHYSICS↗
Weyl invariance with a nontrivial mass scale
A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
z -Weyl gravity in higher dimensions
We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the foliation preserving diffeomorphism invariance adapted to the extra dimensions, thus keeping the general covariance only for the four dimensional spacetime. The conformally invariant gravity can be constructed with an extra (Weyl) scalar field and a real parameter z which describes the degree of anisotropy of conformal transformation between the spacetime and extra dimensional metrics. In the zero mode effective 4D action, it reduces to four-dimensional scalar-tensor theory coupled with nonlinear sigma model described by extra dimensional metrics. There are no restrictions on the value of z at the classical level and possible applications to the cosmological constant problem with a specific choice of z are discussed.
79 ASTRONOMY AND ASTROPHYSICS↗
Bouncing theory in the modified Weyl gravity and its stability conditions
Highlights: •The standard Weyl gravity model is investigated. •The stability conditions of the standard Weyl gravity model are considered. •In the spatially flat Friedmann–Robertson–Walker (FRW) universe, according to the Holographic Dark Energy (HDE) model, the accelerated expansion of the universe is considered. •The suitable conditions of a successful bounce are obtained. -- Abstract: In this paper, we demonstrate the analytical functions of a chameleon scalar field adjust the stability conditions of the standard Weyl gravity model. The suitable conditions of a successful bounce are obtained when the equation of state (EoS) parameter, crosses over the phantom divider. The accelerated expansion of the universe is considered by using the conditions and coordinates of a Friedmann–Robertson–Walker (FRW) universe and the Holographic Dark Energy (HDE) model. The stability conditions of the resulting model are then considered.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗