Scale Invariance in Cosmological Theories
Summary
Scale invariance, the absence of fundamental length or mass scales in a theory’s action, plays a pivotal rˆole in modern cosmology. In global formulations it serves as a custodial symmetry that protects large hierarchies, while in gauged (local) realisations it unifies conformal geometry with gravity by introducing a Weyl gauge field. Spontaneous breaking of scale invariance via a dilaton vacuum expectation value dynamically generates the Planck mass, the cosmological constant and particle masses, providing natural mechanisms for inflation and late-time acceleration. Conformal anomalies in curved space-time can explicitly break this symmetry, shaping effective potentials and vacuum energy. Recent advances explore non-metric geometries in which non-metricity replaces curvature as the geometric origin of all mass scales, and investigate environmental screening effects that reconcile light scalar degrees of freedom with laboratory and astrophysical tests. This interplay of symmetry, geometry and cosmology offers fresh insights into the early Universe, structure formation and the hierarchy problem.
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Scale Invariance in Cosmological Theories publication trend
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Technical terms
Scale invariance: The property of a physical system whose laws remain unchanged under a global rescaling of lengths and energies.
Conformal symmetry: A local extension of scale invariance in which transformations preserve angles while allowing position-dependent scaling of the metric.
Weyl gauge field: The vector field introduced to gauge local scale transformations, ensuring invariance under position-dependent rescalings.
Non-metricity: A geometric feature of a connection whereby the covariant derivative of the metric tensor is nonzero, enabling mass scales to emerge from geometry.
Dilaton: The scalar field that acquires a vacuum expectation value in spontaneously broken scale-invariant theories, generating fundamental mass scales.
Screening mechanism: A phenomenon by which light scalar fields evade experimental constraints through environment-dependent suppression of their interactions.
References
- Higgs‐induced screening mechanisms in scalar‐tensor theories. Annals of the New York Academy of Sciences (2023).
- Weyl conformal geometry vs Weyl anomaly. Journal of High Energy Physics (2023).
- Non-metric geometry as the origin of mass in gauge theories of scale invariance. European Physical Journal C (2023).
- Manifestly scale-invariant regularization and quantum effective operators. Physical Review D (2016).
- Weyl gauge symmetry and its spontaneous breaking in the standard model and inflation. Physical Review D (2019).
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