Cosmic analogues of classic variational problems

TL;DR

This paper explores classical variational problems that serve as analogues to cosmological models, revealing connections between mechanics and universe evolution, including solutions resembling both standard and exotic cosmologies.

Contribution

It identifies and analyzes the cosmic analogues of classical variational problems, linking mechanics solutions to cosmological equations and phenomena.

Findings

Some solutions correspond to main cosmological models

Others resemble exotic cosmologies with phantom fluids

Solutions include models with finite future singularities

Abstract

Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.