Foundational Mass-Distance Scaling Relationships in Cosmology: A Unified Framework for Understanding Dark Phenomena

Foundational Mass-Distance Scaling Relationships in Cosmology: A Unified Framework for Understanding Dark Phenomena

Abstract

The standard ΛCDM model requires approximately 95% of the universe’s energy content to consist of dark matter and dark energy—substances that have never been directly detected despite decades of sophisticated searches. This paper develops a theoretical framework based on fundamental mass-distance scaling relationships that potentially eliminates the need for these exotic components. We propose that cosmic evolution follows exponential scaling laws M(t) = M₀e⁻ᵏᵗ and R(t) = R₀eᵏᵗ, where mass decreases while distances increase over cosmic time with characteristic rate k ≈ 10⁻³³ s⁻¹. These relationships emerge naturally from the mathematical structure of cosmological physics and provide elegant explanations for galaxy rotation curves, cosmic acceleration, and large-scale structure formation without invoking dark matter or dark energy. The framework maintains consistency with general relativity while suggesting that apparent “dark” phenomena result from the geometric effects of universal scaling rather than exotic matter. We establish observational constraints on the scaling parameter k and demonstrate how this approach resolves long-standing puzzles in cosmology while making specific, testable predictions for future observations.

Keywords: cosmological scaling, dark matter, dark energy, exponential expansion, mass-distance relationships

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Introduction

Modern cosmology faces an extraordinary conceptual challenge: the standard model requires that approximately 95% of the universe consists of substances that have never been directly observed. Dark matter, comprising roughly 27% of cosmic energy density, was postulated to explain galaxy rotation curves and large-scale structure formation but remains undetected despite extensive experimental searches. Dark energy, accounting for 68% of the universe, was introduced to explain cosmic acceleration but its physical nature remains completely mysterious.

The introduction of these components, while observationally motivated, represents a fundamental departure from the principle of scientific parsimony. This paper explores an alternative approach: rather than postulating new forms of matter and energy, we investigate whether apparent “dark” phenomena could result from fundamental scaling relationships governing cosmic evolution.

Mathematical Framework

The fundamental ansatz of this framework is that cosmic evolution follows universal exponential scaling laws governing the relationship between mass and distance over cosmic time. We propose:

Mass Evolution: M(t) = M₀ exp(-kt)

Distance Evolution: R(t) = R₀ exp(kt)

where k is a universal scaling parameter with dimensions of inverse time, and t represents cosmic time since some initial epoch.

These relationships suggest that what we interpret as dark matter effects (galactic rotation curves) and dark energy effects (cosmic acceleration) may be geometric consequences of universal scaling rather than evidence for exotic substances. The framework maintains consistency with general relativity while offering a conceptually simpler picture of cosmic evolution.

Key Contributions

Applications

This framework provides explanations for:

This framework is closely connected to other work in Ben’s research portfolio:

References

See the full paper for complete bibliography and citations.

This research paper is part of Ben’s ongoing work in theoretical physics and cosmology.