[Paper Review] Cosmological Consequences of Conformal General Relativity

Danilo Behnke, D. Blaschke+3 more|ArXiv.org|Nov 26, 2000

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper proposes a conformal general relativity (CGR) framework where gravity and matter are unified via a conformal-invariant scalar field (dilaton), offering new explanations for cosmic phenomena such as the arrow of time, dark matter, and accelerated expansion. By treating the universe in Weyl's geometry of similarity, CGR explains redshift as atomic mass growth rather than spacetime expansion, and derives a naturally accelerating dust phase consistent with supernova data without a cosmological constant.

ABSTRACT

We consider cosmological consequences of a conformal-invariant unified theory which is dynamically equivalent to general relativity and is given in a space with the geometry of similarity. We show that the conformal-invariant theory offers new explanations for to such problems as the arrow of time, initial cosmic data, dark matter and accelerating evolution of the universe in the dust stage.

Motivation & Objective

• To resolve foundational issues in cosmology—such as the arrow of time, initial conditions, and dark matter—by reinterpreting general relativity in a conformal-invariant framework.
• To show that the standard model of cosmology can be reinterpreted using Weyl's geometry of similarity, replacing Riemannian geometry as the physical standard of measurement.
• To demonstrate that the observed cosmic acceleration in the dust phase arises naturally from the conformal dynamics of the dilaton field, without requiring dark energy or quintessence.
• To explain the apparent missing mass in the universe as a consequence of retarded particle mass growth in the past, reconciling low observed matter density with current values.
• To establish a dynamical, quantum-compatible cosmology where the wave function of the universe evolves via conformal-invariant Bogoliubov quasiparticles.

Proposed method

• Formulates a conformal-invariant action combining the Penrose-Chernikov-Tagirov dilaton action with matter Lagrangians that generate particle masses via the scalar field Φ.
• Applies Lichnerowicz conformal-invariant variables to define physical observables in the geometry of similarity, replacing absolute Riemannian intervals with relative, conformally invariant ratios.
• Derives two cosmological pictures: one for Einstein observers (FRW with spacetime expansion) and one for Weyl observers (Hoyle-Narlikar-type with evolving atomic masses).
• Uses the dilaton field φ(T) as a conformal time variable, with φ(T₀) = T₀²/4 · ρ̄_D in the dust stage, leading to a Hubble parameter H₀ = 2/T₀.
• Computes the acceleration parameter q = -1/2 from the conformal evolution of the dilaton, matching recent supernova data.
• Estimates the matter density retardation factor γ = 3 for the dust stage, showing that Ω₀ ≈ γ · Ω₀^exp ≈ 1 when Ω₀^exp ≈ 0.3, resolving the missing energy problem without dark energy.

Experimental results

Research questions

• RQ1 Can the arrow of time be derived from conformal invariance and the stability of a physical system, rather than being postulated?
• RQ2 How does the geometry of similarity in Weyl’s framework alter the interpretation of cosmological redshift and Hubble’s law compared to standard GR?
• RQ3 Can the observed cosmic acceleration in the dust phase be explained without introducing a cosmological constant or quintessence?
• RQ4 Does the conformal-invariant evolution of the dilaton field account for the apparent dark matter density by reflecting past particle mass reduction?
• RQ5 Is the observed matter density in the present universe consistent with a conformal cosmology where particle masses increase over time?

Key findings

• The conformal-invariant theory leads to a naturally accelerating dust phase with an acceleration parameter q = -1/2, consistent with observations from the Supernova Cosmology Project.
• The present-day matter density Ω₀ ≈ 1 is explained as Ω₀ = γ · Ω₀^exp with γ = 3, reconciling the observed Ω₀^exp ≈ 0.3 with a flat universe without invoking dark energy.
• Redshift Z > 1 is interpreted as a consequence of increasing atomic masses due to the dilaton field, not spacetime expansion, offering an alternative to the standard FRW interpretation.
• The Hubble parameter in the dust stage is H₀ = 2/T₀, derived from the conformal evolution φ(T₀) = T₀²/4 · ρ̄_D, matching the observed Hubble flow.
• The wave function of the universe is constructed from conformal-invariant Bogoliubov quasiparticle states, yielding a consistent quantum cosmological framework.
• The Planck mass is recovered as the present value of the dilaton field φ(T₀) = √ρ̄_R · T₀, showing consistency with observational data within error bounds.