Non-metric geometry as the origin of mass in gauge theories of scale invariance

Abstract

We discuss gauge theories of scale invariance beyond the Standard Model (SM) and Einstein gravity. A consequence of gauging this symmetry is that their underlying 4D geometry is non-metric (${\nabla }_{\mu }{g}_{\alpha \beta }\ne 0$). Examples of such theories are Weyl's {\it original} quadratic gravity theory and its Palatini version. These theories have spontaneous breaking of the gauged scale symmetry to Einstein gravity. All mass scales have a geometric origin: the Planck scale ($M_p$), cosmological constant ($\Lambda$) and the mass of the Weyl gauge boson (${\omega }_{\mu }$) of scale symmetry are proportional to a scalar field vev that has an origin in the (geometric) ${\tilde{R}}^2$ term in the action. With ${\omega }_{\mu }$ of non-metric geometry origin, the SM Higgs field also has a similar origin, generated by Weyl boson fusion in the early Universe. This appears as a microscopic realisation of "matter creation from geometry" discussed in the thermodynamics of open systems applied to cosmology. Unlike in local scale invariant theories (no ${\omega }_{\mu }$ present) with an underlying pseudo-Riemannian geometry, in our case: 1) there are no ghosts and no additional fields beyond the SM and underlying Weyl or Palatini geometry, 2) the cosmological constant is positive and is small because gravity is weak, 3) the Weyl or Palatini connection shares the Weyl (gauge) symmetry of the action, and: 4) there exists a non-trivial, conserved Weyl current of this symmetry. An intuitive picture of non-metricity and its relation to mass generation is also provided from a solid state physics perspective where it is common and is associated with point defects (metric anomalies) of the crystalline structure.

25 pages, LaTex

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• Cosmological implications of the Weyl geometric gravity theory
• Weyl geometric effects on the propagation of light in gravitational fields
• Length-preserving biconnection gravity and its cosmological implications
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Thermodynamics of the Weyl Geometric Gravity Black Holes
• Big Bang Nucleosynthesis constraints on the cosmological evolution in a Universe with a Weylian Boundary
• Observational Constraints on Extended Starobinsky and Weyl Gravity Model of Inflation
• Spontaneous scale symmetry breaking at high temperature
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
• Mimetic Weyl geometric gravity
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Observational tests of the conformal osculating Barthel-Kropina cosmological model
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• Revisiting local-scale invariant gravitational theory
• Cosmological test of a length-preserving biconnection gravity
• The Weyl Geometric Gravity black hole in light of the Solar System tests