[Paper Review] The derivation of the coupling constant in the new Self Creation Cosmology

Garth A. Barber|ArXiv.org|Feb 21, 2003

Cosmology and Gravitation Theories4 references3 citations

TL;DR

This paper derives the Brans-Dicke coupling constant ω = -3/2 in the Self Creation Cosmology (SCC) framework through consistency between Mach's Principle and local energy conservation. By enforcing mutual interaction between matter and the scalar field and ensuring agreement with General Relativity in standard tests, the theory uniquely determines ω as an inherent consequence of its foundational principles, not an arbitrary input.

ABSTRACT

It has been shown that the new Self Creation Cosmology theory predicts a universe with a total density parameter of one third yet spatially flat, which would appear to accelerate in its expansion. Although requiring a moderate amount of 'cold dark matter' the theory does not have to invoke the hypotheses of inflation, 'dark energy', 'quintessence' or a cosmological constant (dynamical or otherwise) to explain observed cosmological features. The theory also offers an explanation for the observed anomalous Pioneer spacecraft acceleration, an observed spin-up of the Earth and an problematic variation of G observed from analysis of the evolution of planetary longitudes. It predicts identical results as General Relativity in standard experimental tests but three definitive experiments do exist to falsify the theory. In order to match the predictions of General Relativity, and observations in the standard tests, the new theory requires the Brans Dicke omega parameter that couples the scalar field to matter to be -3/2 . Here it is shown how this value for the coupling parameter is determined by the theory's basic assumptions and therefore it is an inherent property of the principles upon which the theory is based.

Motivation & Objective

• To establish the theoretical derivation of the Brans-Dicke coupling parameter ω in the Self Creation Cosmology (SCC) framework.
• To demonstrate that ω = -3/2 is not an empirical adjustment but a necessary outcome of the theory’s core principles: Mach’s Principle and local energy conservation.
• To resolve the apparent arbitrariness of setting ω = -3/2 to match General Relativity in standard tests by deriving it from first principles.
• To ensure consistency between the scalar field equation, the matter energy-momentum conservation law, and the gravitational field equations in SCC.
• To show that the resulting field equations reproduce the predictions of General Relativity in solar system tests while allowing for a different cosmological and dynamical framework.

Proposed method

• Imposes the Principle of Mutual Interaction (PMI), where matter energy-momentum divergence is proportional to the scalar field's d’Alembertian, linking matter and scalar field dynamics.
• Applies the Local Conservation of Energy principle, asserting that gravitational potential energy is absorbed into particle rest mass, leading to a variable rest mass dependent on the scalar field.
• Derives the scalar field solution from both the field equation (Box φ = 4πT_M^σσ) and the energy conservation condition, requiring consistency between the two.
• Uses the spherically symmetric one-body solution to match the scalar field behavior at infinity and in the weak-field limit.
• Compares the effective gravitational acceleration from the metric and scalar field equations with the acceleration derived from energy conservation, imposing consistency conditions.
• Solves the resulting system of three equations (128, 129, 132) for λ, κ, and ψ, yielding unique values λ = 1, κ = 1, ψ = 1, which then determine ω.

Experimental results

Research questions

• RQ1 Why is the Brans-Dicke coupling parameter ω = -3/2 required in the Self Creation Cosmology to match General Relativity in standard tests?
• RQ2 Can the value of ω be derived from the theory’s foundational principles rather than being empirically imposed?
• RQ3 How do the principles of Mach’s Principle and local energy conservation constrain the parameters λ, κ, and ψ in the SCC framework?
• RQ4 What conditions ensure consistency between the scalar field equation and the energy-mass conservation law in the one-body problem?
• RQ5 What is the unique solution for the coupling parameters that simultaneously satisfies the field equations, energy conservation, and observational consistency?

Key findings

• The coupling parameter ω is uniquely determined as ω = -3/2 through the consistency of the scalar field equation and the energy conservation law, not by arbitrary choice.
• The parameters λ = 1, κ = 1, and ψ = 1 are derived as the unique solution to the system of equations from field consistency and energy conservation.
• The scalar field solution from the field equation (φ ∝ exp[2λ/(2+λ−κλ²) GM/r]) matches the solution from energy conservation (φ ∝ exp[GM/r]) only when λ = 1, κ = 1, ψ = 1.
• The Newtonian gravitational constant G_N is confirmed as the limit of φ⁻¹ at infinity, ensuring consistency with Cavendish-type experiments.
• With ω = -3/2, the theory’s field equations reduce to a form that reproduces General Relativity in the weak-field limit and solar system tests.
• The value ω = -3/2 ensures that the Jordan frame (JF) of the theory conserves mass-energy and the Einstein frame (EF) conserves energy-momentum, with both frames being physically meaningful.