Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation

Abstract

We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the Standard Model (SM) and inflation. In models with non-minimal couplings of the scalar fields to the Ricci scalar, that are conformal invariant, the spontaneous generation by a scalar field(s) vev of a positive Newton constant demands a negative kinetic term for the scalar field, or vice-versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field ${\omega }_{\mu }$ couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field ${\omega }_{\mu }$ undergoes a Stueckelberg mechanism and becomes massive after "eating" the (radial mode) would-be-Goldstone field (dilaton $\rho$) in the scalar sector. Before the decoupling of ${\omega }_{\mu }$, the dilaton can act as UV regulator and maintain the Weyl symmetry at the {\it quantum} level, with relevance for solving the hierarchy problem. After the decoupling of ${\omega }_{\mu }$, the scalar potential depends only on the remaining (angular variables) scalar fields, that can be the Higgs field, inflaton, etc. We show that successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with ${\omega }_{\mu }$ introduced to avoid ghosts, the natural framework is that of Weyl geometry which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.

19 pages, v3: correction in Section 4, added figures; conclusions unchanged

References in corpus (12)

• Quantum scale invariance, cosmological constant and hierarchy problem
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential
• No fifth force in a scale invariant universe
• On the geometrical interpretation of scale-invariant models of inflation
• Stueckelberg breaking of Weyl conformal geometry with applications to gravity
• A note on Gauge Theories Coupled to Gravity
• Implication of Compensator Field and Local Scale Invariance in the Standard Model
• Two-loop scale-invariant scalar potential and quantum effective operators
• Ultra-weak sector, Higgs boson mass, and the dilaton
• The unexpected resurgence of Weyl geometry in late 20-th century physics
• Frozen up Dilaton and the GUT/Planck Mass Ratio

Cited by in corpus (55)

• 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
• Stueckelberg breaking of Weyl conformal geometry with applications to gravity
• 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
• Scale independent $R^2$ inflation
• Planck mass and inflation as consequences of dynamically broken 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
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Unitary inflaton as decaying dark matter
• Coupling matter and curvature in Weyl geometry: conformally invariant $f\left(R,L_m\right)$ gravity
• Minimal $k$-inflation in light of the conformal metric-affine geometry
• Scale and Weyl Invariance in Einstein-Cartan Gravity
• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Weyl Scaling Invariant $R^2$ Gravity for Inflation and Dark Matter
• Unified Emergence of Energy Scales and Cosmic Inflation
• Compact stellar structures in Weyl geometric gravity
• Inflation in Weyl-invariant Einstein-Cartan gravity
• The origin of Weyl gauging in metric-affine theories
• A Walking Dilaton Inflation
• Projective transformations in metric-affine and Weylian geometries
• Scale Invariant Gravity and Black Hole Ringdown
• Cosmological implications of the Weyl geometric gravity theory
• Weyl geometric effects on the propagation of light in gravitational fields
• Renormalization Group for Non-minimal ${\varphi }^{2}R$ Couplings and Gravitational Contact Interactions
• Conformal $\alpha$-attractor Inflation with Weyl Gauge Field
• Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory
• Inflation with Massive Spin-2 Ghosts
• Inflation and dark matter after spontaneous Planck scale generation by hidden chiral symmetry breaking
• BRST Formalism of Weyl Conformal Gravity
• Inflation in Weyl Scaling Invariant Gravity with $R^3$ Extensions
• Conformally covariant operators of mixed-symmetry tensors and MAGs
• Gravitational Waves from Preheating in Inflation with Weyl Symmetry
• Modified gravity from Weyl connection and the $f(R,\mathcal{A})$ extension
• Spacetime and Planck mass generation from scale-invariant degenerate gravity
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Cosmological evolution in Weyl conformal geometry
• Spontaneous scale symmetry breaking at high temperature
• Observational Constraints on Extended Starobinsky and Weyl Gravity Model of Inflation
• Dilaton-induced variations in Planck constant and speed of light: An alternative to Dark Energy
• Mimetic Weyl geometric gravity
• Observational tests of the conformal osculating Barthel-Kropina cosmological model
• Planck Scale from Broken Local Conformal Invariance in Weyl Geometry
• Probing Primordial Symmetry Breaking with Cosmic Microwave Background Anisotropy
• On Conformal Transformation with Multiple Scalar Fields and Geometric Property of Field Space with Einstein-like Solutions
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• Jacobi stability of circular orbits around conformally invariant Weyl gravity black holes
• Inflation in light of ACT/SPT: A new perspective from Weyl gravity
• Warm inflation in Weyl geometric gravity
• $f(R)$ gravity with broken Weyl gauge symmetry, cosmological backreaction, and its effects on CMB anisotropy
• Lost in translation: the Abelian affine connection (in the coincident gauge)
• The Weyl Geometric Gravity black hole in light of the Solar System tests