Particle-Like Description in Quintessential Cosmology

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.

35 pages, 26 figures, RevTeX4, some applications of our treatment to investigation of quintessence models were added

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• Escaping the Big Rip?
• Energy conditions and current acceleration of the universe
• Direct evidence of acceleration from distance modulus redshift graph
• Phantom cosmology as a simple model with dynamical complexity
• FRW Cosmological model with Modified Chaplygin Gas and Dynamical System
• Reconstruction of scalar potentials in two-field cosmological models
• Dynamical dark energy models -- dynamical system approach
• Phantom cosmology as a scattering process
• Cosmological zoo -- accelerating models with dark energy
• Two-field cosmological models and large-scale cosmic magnetic fields
• Modified Friedmann Cosmologies - theory & observations
• Fomin's conception of quantum cosmogenesis
• The relation between Geometry and Matter in classical and quantum Gravity and Cosmology