The Weyl Anomaly and the Nature of the Background Geometry (original) (raw)

Weyl anomalies and the nature of the gravitational field

arXiv: High Energy Physics - Theory, 2019

The presence of gravity generalizes the notion of scale invariance to Weyl invariance, namely, invariance under local rescalings of the metric. In this work, we have computed the Weyl anomaly for various classically scale or Weyl invariant theories, making particular emphasis on the differences that arise when gravity is taken as a dynamical fluctuation instead of as a non-dynamical background field. We find that the value of the anomaly for the Weyl invariant coupling of scalar fields to gravity is sensitive to the dynamical character of the gravitational field, even when computed in constant curvature backgrounds. We also discuss to what extent those effects are potentially observable.

Cosmological evolution in Weyl conformal geometry

2021

We discuss the cosmological evolution of the Weyl conformal geometry and its associated Weyl quadratic gravity. The Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity; this happens after the Weyl gauge field (ωμ) of scale symmetry, that is part of the Weyl geometry, becomes massive by Stueckelberg mechanism and decouples. This breaking is a natural result of the cosmological evolution of Weyl geometry, in the absence of matter. The Weyl quadratic gravity provides an accelerated expansion of the Universe controlled by the scalar mode of the R̃ term in the action and by ω0. The comparison to the ΛCDM model shows a very good agreement between these two models for the (dimensionless) Hubble function h(z) and the deceleration q(z) for redshift z ≤ 3. Therefore, the Weyl conformal geometry and its associated Weyl quadratic gravity provide an interesting alternative to the ΛCDM model and to the Einstein gravity. ∗E-mail: ...

Twenty years of the Weyl anomaly

Classical and Quantum Gravity, 1994

In 1973 two Salam protégés (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor g µν (x) → Ω 2 (x)g µν (x) displayed by classical massless field systems in interaction with gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic review.

On the physical consequences of a Weyl invariant theory of gravity

2020

In this paper we explore the physical consequences of assuming Weyl invariance of the laws of gravity from the classical standpoint exclusively. Actual Weyl invariance requires to replace the underlying Riemannian geometrical structure of the background spacetimes by Weyl integrable geometry (WIG). We show that gauge freedom, a distinctive feature of Weyl invariant theories of gravity, leads to very unusual consequences. For instance, within the cosmological setting in a WIG-based conformal invariant gravity theory, also known as conformal general relativity (CGR), a static universe is physically equivalent to a universe undergoing de Sitter expansion. It happens also that spherically symmetric black holes are physically equivalent to singularity-free wormholes. Another outstanding consequence of gauge freedom in the framework of CGR is that inflation is not required to explain the flatness, horizon and relict particle abundances, among other puzzles that arise in standard GR-based ...

The cosmological constant and Pioneer anomaly from Weyl spacetimes and Mach’s principle

It is shown how Weyl's geometry and Mach's holographic principle furnishes both the magnitude and sign (towards the sun) of the Pioneer anomalous acceleration a P ∼ −c 2 /R Hubble firstly observed by Anderson et al. Weyl's geometry can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan-Brans-Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. A nonvanishing value of the vacuum energy density of the order of 10 −123 M 4 Planck is found consistent with observations. Weyl's geometry accounts also for the phantom scalar field in modern Cosmology in a very natural fashion.

Dark matter as a Weyl geometric effect

Physical Review D

We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type geometry, and its associated conformally invariant Weyl geometric quadratic gravity. As a first step in our investigations we write down the simplest possible conformally invariant gravitational action, constructed in Weyl geometry, and containing the Weyl scalar, and the strength of the Weyl vector only. By introducing an auxiliary scalar field, the theoretical model can be reformulated in the Riemann geometry as scalar-vector-tensor theory, containing a scalar field, and the Weyl vector, respectively. The field equations of the theory are derived in the metric formalism, in the absence of matter. A specific static, spherically symmetric model, in which the Weyl vector has only a radial component, is considered. In this case, an exact analytic solution of the gravitational field equations can be obtained. The behavior of the galactic rotation curves is also considered in detail, and it is shown that an effective geometric mass term, with an associated density profile, can also be introduced. Three particular cases, corresponding to some specific functional forms of the Weyl vector, are also investigated. A comparison of the model with a selected sample of galactic rotation curves is also performed when an explicit breaking of conformal invariance is introduced, which allows the fix of the numerical values of the free parameters of the model. Our results show that Weyl geometric models can be considered as a viable theoretical alternative to the dark matter paradigm.

On the cosmological solutions in Weyl geometry

Journal of Cosmology and Astroparticle Physics, 2021

We investigated the possibility of construction the homogeneous and isotropic cosmological solutions in Weyl geometry. We derived the self-consistency condition which ensures the conformal invariance of the complete set of equations of motion. There is the special gauge in choosing the conformal factor when the Weyl vector equals zero. In this gauge we found new vacuum cosmological solutions absent in General Relativity. Also, we found new solution in Weyl geometry for the radiation dominated universe with the cosmological term, corresponding to the constant curvature scalar in our special gauge. Possible relation of our results to the understanding both dark matter and dark energy is discussed.

Anomaly-Free Special Weyl Symmetry

2022

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the conformal symmetry. Besides that, the fundamental theory must include gravity, whereas all known extensions of the conformal invariance to the curved space-time suffer from the Weyl anomaly. We propose an extension of the flat space conformal invariance to the curved space-time which is anomaly-free. We discuss how the effective Lagrangian respecting this special Weyl symmetry can be used for the description of particle phenomenology and cosmology.

Gravitational and Weyl anomalies

Physics Letters B, 1984

We discuss the anomaly structure of diffeomorphisms in four dimensions. In particular we prove that a mixed gravitational-abelian gauge anomaly can be avoided and replaced by a mixed Lorentz-U(1) anomaly. The remaining anomalies of the diffeomorphisms can be replaced by Weyl anomalies.

Some cosmological consequences of Weyl invariance

Journal of Cosmology and Astroparticle Physics, 2015

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.