Stueckelberg breaking of Weyl conformal geometry with applications to gravity

Abstract

Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian geometry after a Weyl gauge transformation (of "gauge fixing") while Stueckelberg mechanism re-arranges the degrees of freedom, conserving their number ($n_{df}$). The Weyl gauge field (${\omega }_{\mu }$) of local scale transformations acquires a mass after absorbing a compensator (dilaton), decouples, and Weyl connection becomes Riemannian. Mass generation has thus a dynamic origin, as a transition from Weyl to Riemannian geometry. We show that a "gauge fixing" symmetry transformation of the original Weyl quadratic gravity action in its Weyl geometry formulation immediately gives the Einstein-Proca action for the Weyl gauge field and a positive cosmological constant, plus matter action (if present). As a result, the Planck scale is an {\it emergent} scale, where Weyl gauge symmetry is spontaneously broken and Einstein action is the broken phase of Weyl action. This is in contrast to local scale invariant models (no gauging) where a negative kinetic term (ghost dilaton) remains present and $n_{df}$ is not conserved when this symmetry is broken. The mass of ${\omega }_{\mu }$, setting the non-metricity scale, can be much smaller than $M_{\text{Planck}}$, for ultraweak values of the coupling ($q$). If matter is present, a positive contribution to the Planck scale from a scalar field (${\varphi }_1$) vev induces a negative (mass)${}^2$ term for ${\varphi }_1$ and spontaneous breaking of the symmetry under which it is charged. These results are immediate when using a Weyl geometry formulation of an action instead of its Riemannian picture. Briefly, Weyl gauge symmetry is physically relevant and its role in high scale physics should be reconsidered.

13 pages

References in corpus (12)

• Quantum scale invariance, cosmological constant and hierarchy problem
• The Higgs Phenomenon in Quantum Gravity
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential
• Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation
• Weyl $R^2$ inflation with an emergent Planck scale
• Implication of Compensator Field and Local Scale Invariance in the Standard Model
• Probing the small distance structure of canonical quantum gravity using the conformal group
• Conformal vector dark matter and strongly first-order electroweak phase transition
• Inflation as a spontaneous symmetry breaking of Weyl symmetry
• Weyl Symmetry Inspired Inflation and Dark Matter
• Local Conformal Symmetry: the Missing Symmetry Component for Space and Time

Cited by in corpus (41)

• Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation
• Gauging scale symmetry and inflation: Weyl versus Palatini gravity
• Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
• Standard Model in Weyl conformal geometry
• Weyl $R^2$ inflation with an emergent Planck scale
• Black hole solutions in the quadratic Weyl conformal geometric theory of gravity
• Dark matter as a Weyl geometric effect
• Non-metric geometry as the origin of mass in gauge theories of scale invariance
• Cosmological evolution and dark energy in osculating Barthel-Randers geometry
• Palatini formulation of the conformally invariant $f\left(R,L_m\right)$ gravity theory
• Cosmological tests of the osculating Barthel-Kropina dark energy model
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Dark energy and accelerating cosmological evolution from osculating Barthel-Kropina geometry
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• Scale and Weyl Invariance in Einstein-Cartan Gravity
• Compact stellar structures in Weyl geometric gravity
• Curvature-matter couplings in modified gravity: from linear models to conformally invariant theories
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Projective transformations in metric-affine and Weylian geometries
• Weyl geometric effects on the propagation of light in gravitational fields
• Cosmological implications of the Weyl geometric gravity theory
• Introduction to Quantization of Conformal Gravity
• Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory
• Renormalization Group for Non-minimal ${\varphi }^{2}R$ Couplings and Gravitational Contact Interactions
• Conformal Metric-Affine Gravities
• Dissipative quintessence, and its cosmological implications
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Modified gravity from Weyl connection and the $f(R,\mathcal{A})$ extension
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Cosmic inflation from broken conformal symmetry
• Higgs Potential from Weyl Conformal Gravity
• Cosmological evolution in Weyl conformal geometry
• Spontaneous scale symmetry breaking at high temperature
• Observational Constraints on Extended Starobinsky and Weyl Gravity Model of Inflation
• Mimetic Weyl geometric gravity
• Emergence of Einstein Gravity from Weyl Gravity
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• Planck Scale from Broken Local Conformal Invariance in Weyl Geometry
• Warm inflation in Weyl geometric gravity
• Revisiting local-scale invariant gravitational theory
• The Weyl Geometric Gravity black hole in light of the Solar System tests