Particle-Like Description in Quintessential Cosmology

Details Particle-Like Description in Quintessential Cosmology Particle-Like Description in Quintessential Cosmology

2003-05-08

arxiv.org/abs/gr-qc/0305033v3

Phys.Rev. D69 (2004) 083518

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevD.69.083518

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.

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