[Paper Review] Cosmological Coincidence Problem in an Einstein Universe and in a Friedman Dust Universe with Einstein's Lambda

James G. Gilson|arXiv (Cornell University)|May 20, 2007

Cosmology and Gravitation Theories10 references3 citations

TL;DR

This paper resolves the cosmological coincidence problem in both the Einstein universe and a Friedman dust universe with Einstein's cosmological constant by identifying a misinterpretation of dark energy density magnitude and epoch timing. By eliminating a degeneracy in measurement epochs, it removes the apparent fine-tuned coincidence between dark and normal matter densities.

ABSTRACT

In this paper, it is shown that the cosmological model that was introduced in a sequence of three earlier papers under the title A Dust Universe Solution to the Dark Energy Problem can be used to analyse and solve the Cosmological Coincidence Problem. The generic coincidence problem that appears in the original Einstein universe model is shown to arise from a misunderstanding about the magnitude of dark energy density and the epoch time governing the appearance of the integer relation between dark energy and normal energy density. The solution to the generic case then clearly points to the source of the time coincidence integer problem in the Friedman dust universe model. It is then possible to eliminate this coincidence by removing a degeneracy between different measurement epoch times.

Motivation & Objective

• To address the cosmological coincidence problem in the original Einstein universe model.
• To identify the root cause of the time coincidence problem in the Friedman dust universe with Einstein's lambda.
• To resolve the apparent fine-tuning between dark energy and normal matter densities by correcting epoch interpretation.
• To eliminate a degeneracy in measurement epoch times that artificially enforces the coincidence.

Proposed method

• Analyzes the dust universe solution to the dark energy problem as presented in prior work.
• Re-evaluates the magnitude of dark energy density and its temporal evolution in the Einstein universe.
• Identifies the epoch at which integer relations between dark and normal energy densities appear as a result of misjudged timing.
• Applies the same reasoning to the Friedman dust universe with Einstein's lambda to expose the same underlying error.
• Removes the degeneracy between different measurement epochs to eliminate the false appearance of coincidence.
• Uses consistency in energy density scaling and epoch-dependent relations to resolve the coincidence.

Experimental results

Research questions

• RQ1 Why does the cosmological coincidence problem arise in the original Einstein universe model?
• RQ2 What causes the apparent time coincidence between dark energy and normal matter densities in the Friedman dust universe with lambda?
• RQ3 How does misjudging the epoch of dark energy density magnitude contribute to the coincidence problem?
• RQ4 Can the coincidence be resolved by redefining or removing degeneracy in measurement epochs?
• RQ5 What role does the magnitude of dark energy density play in the perceived fine-tuning?

Key findings

• The cosmological coincidence problem in the Einstein universe arises from a misinterpretation of the magnitude of dark energy density and the timing of its appearance.
• The integer relation between dark and normal energy densities is not fundamental but results from a miscalculation of the epoch when the densities become comparable.
• In the Friedman dust universe with Einstein's lambda, the same coincidence stems from the same misjudged epoch timing.
• The apparent coincidence is eliminated by removing a degeneracy between different measurement epochs, which artificially enforces the observed relation.
• The resolution demonstrates that the coincidence is not a physical fine-tuning but an artifact of incorrect temporal interpretation.
• The dust universe solution with lambda provides a consistent framework where the coincidence problem vanishes upon proper epoch calibration.