Particle-Like Description in Quintessential Cosmology

TL;DR

This paper models the evolution of the universe with quintessence as a classical particle in a potential, offering a Hamiltonian framework to classify solutions and reconstruct cosmological parameters from supernova data.

Contribution

It introduces a Hamiltonian approach to analyze quintessence cosmology, enabling classification of solutions and potential reconstruction from observational data.

Findings

Hamiltonian method effectively classifies cosmological solutions.

Potential reconstruction from supernova luminosity distances is feasible.

Application to modern cosmological models demonstrates approach's utility.

Abstract

Assuming equation of state for quintessential matter: $p=w(z)\rho$, we analyse dynamical behaviour of the scale factor in FRW cosmologies. It is shown that its dynamics is formally equivalent to that of a classical particle under the action of 1D potential $V(a)$. It is shown that Hamiltonian method can be easily implemented to obtain a classification of all cosmological solutions in the phase space as well as in the configurational space. Examples taken from modern cosmology illustrate the effectiveness of the presented approach. Advantages of representing dynamics as a 1D Hamiltonian flow, in the analysis of acceleration and horizon problems, are presented. The inverse problem of reconstructing the Hamiltonian dynamics (i.e. potential function) from the luminosity distance function $d_{L}(z)$ for supernovae is also considered.