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Updated: Dec 6, 2025

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Future Attractors in 2+1 Dimensional Λ Gravity.

¹Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna.

Physical Review Letters

|October 5, 2020

Summary

Cosmological models with hyperbolic spatial topology evolve towards a de Sitter universe. Gravitation drives this homogenization, regardless of initial conditions, for spacetimes with a positive cosmological constant.

Area of Science:

Cosmology
General Relativity
Mathematical Physics

Background:

Einsteinian spacetime dynamics with a positive cosmological constant are explored.
The role of compact hyperbolic spatial topology in cosmological evolution is investigated.

Purpose of the Study:

To determine the long-term behavior of 2+1 dimensional spacetimes with specific topological and cosmological properties.
To demonstrate the phenomenon of large-data homogenization in cosmological models.

Main Methods:

Analysis of Einsteinian spacetime evolution equations.
Investigating the asymptotic behavior of cosmological models with compact hyperbolic spatial topology.

Main Results:

Spacetimes evolve towards a de Sitter model with homogeneous hyperbolic spatial geometry.

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The de Sitter model acts as a uniform future attractor for these spacetimes.

This homogenization occurs independently of arbitrary large initial data.

Conclusions:

Gravitation enforces late-time homogenization in cosmological evolution.
The initial state of the spacetime does not prevent the eventual homogeneous state.
These findings exemplify large-data homogenization in cosmology.