[Paper Review] Scale invariant gravity and the quasi-static universe

Robin Booth|ArXiv.org|Mar 19, 2002

Cosmology and Gravitation Theories17 references3 citations

TL;DR

This paper proposes a scale-invariant reformulation of General Relativity by replacing Newton's gravitational constant with a scale-dependent renormalization factor, leading to a quasi-static universe model that eliminates the Planck scale and resolves key issues in Big Bang cosmology and quantum gravity. The model predicts a universe without an initial singularity, where proton collapse into black holes marks a final cosmic phase, offering an alternative to inflation and dark matter explanations.

ABSTRACT

We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic scale. We show that many of the problems associated with cosmology and quantum gravity follow directly from this assumption. An alternative scale invariant paradigm is proposed, in which the appropriate scale for General Relativity takes the Universe as its baseline, and the gravitational force does not have any fixed relationship to forces that apply on the atomic scale. It is shown that this gives rise to a quasi-static universe, and that the predicted behaviour of this model can resolve most of the problems associated with the standard Big Bang model. The replacement of Newton's gravitational constant in the quasi-static model by a scale-dependent re-normalisation factor is also able to account for a number of astronomical observations that would otherwise require ad-hoc explanations. Some of the implications of scale invariant gravity for Planck scale physics, quantum cosmology, and the nature of time are discussed.

Motivation & Objective

• To address the fundamental lack of scale invariance in General Relativity, which ties gravitational dynamics to atomic-scale physics via Newton's constant G.
• To resolve long-standing problems in cosmology and quantum gravity, such as the hierarchy problem and the initial singularity, by redefining the gravitational scale using cosmological units.
• To eliminate the Planck scale as a fundamental physical scale, thereby challenging the necessity of a canonical quantum gravity framework.
• To explore the implications of scale invariance for the nature of time, quantum cosmology, and the ultimate fate of the universe.

Proposed method

• Reformulate the Einstein-Hilbert action by removing the 16πG factor, enabling scale invariance under conformal transformations g′αβ = Ω²gαβ and R′ = Ω⁻²R.
• Introduce a scale-dependent renormalization factor for G, replacing the constant G with a dynamical quantity tied to the universe’s scale factor.
• Derive modified gravitational field equations that describe a universe that is either static or expanding depending on the observer’s reference frame.
• Use cosmological units as the baseline scale for gravity, replacing the atomic scale as the fundamental reference.
• Apply the model to predict cosmic evolution, including the point where proton Compton wavelength equals its Schwarzschild radius.
• Analyze implications for quantum gravity, time, and the ultimate fate of the universe, including black hole formation from proton collapse.

Experimental results

Research questions

• RQ1 Can a scale-invariant formulation of General Relativity eliminate the need for the Planck scale and resolve the hierarchy problem between atomic and gravitational scales?
• RQ2 Does a quasi-static universe model based on cosmological-scale gravity naturally account for observed astronomical phenomena without requiring dark matter or inflation?
• RQ3 How does the dynamical renormalization of Newton’s constant affect the early universe’s evolution and the formation of particle masses?
• RQ4 What are the implications of scale invariance for the nature of time and the canonical quantization of gravity?
• RQ5 Can the model predict a final cosmic state where protons collapse into micro black holes, suggesting a cyclic or multiverse-like evolution?

Key findings

• The model eliminates the initial Big Bang singularity by replacing the fixed Planck scale with a scale-dependent gravitational constant, leading to a quasi-static universe.
• At time n = N (where N is the baryon number), the proton’s Compton wavelength equals its Schwarzschild radius, implying that protons collapse into micro black holes.
• The gravitational structure constant is predicted to vary over time, suggesting a dynamic unification of electromagnetic and gravitational self-energy at early epochs.
• The model removes the need for a fundamental Planck scale, challenging the foundation of canonical quantum gravity and suggesting gravity may emerge from matter fields.
• The universe’s dynamics are frame-dependent: static in cosmological coordinates, expanding in atomic time, resolving the tension between static and evolving cosmologies.
• The theory provides an alternative explanation for astronomical observations traditionally attributed to dark matter or inflation, via a naturally scale-invariant gravitational framework.