General solutions for flat Friedmann universe filled by perfect fluid and scalar field with exponential potential

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dc.creatorDehnen, H.
dc.creatorGavrilov, V. R.
dc.creatorMelnikov, V. N.
dc.date2002-12-26
dc.date.accessioned2026-07-07T03:27:27Z
dc.date.available2026-07-07T03:27:27Z
dc.descriptionWe study integrability by quadrature of a spatially flat Friedmann model containing both a minimally coupled scalar field $ϕ$ with an exponential potential $V(ϕ)\sim\exp[-\sqrt{6}σκϕ]$, $κ=\sqrt{8πG_N}$, of arbitrary sign and a perfect fluid with barotropic equation of state $p=(1-h)ρ$. From the mathematical view point the model is pseudo-Euclidean Toda-like system with 2 degrees of freedom. We apply the methods developed in our previous papers, based on the Minkowsky-like geometry for 2 characteristic vectors depending on the parameters $σ$ and $h$. In general case the problem is reduced to integrability of a second order ordinary differential equation known as the generalized Emden-Fowler equation, which was investigated by discrete-group methods. We present 4 classes of general solutions for the parameters obeying the following relations: {\bf A}. $σ$ is arbitrary, $h=0$; {\bf B}. $σ=1-h/2$, $0<h<2$; {\bf C1}. $σ=1-h/4$, $0<h\leq 2$; {\bf C2}. $σ=|1-h|$, $0<h\leq 2$, $h\neq 1,4/3$. We discuss the properties of the exact solutions near the initial singularity and at the final stage of evolution.
dc.description13 pages, Latex, 1 figure, submit. to Class. Quantum Grav
dc.identifierhttps://arxiv.org/abs/gr-qc/0212107
dc.identifierhttp://arxiv.org/abs/gr-qc/0212107
dc.identifierGrav.Cosmol. 9 (2003) 189-195
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34440
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleGeneral solutions for flat Friedmann universe filled by perfect fluid and scalar field with exponential potential
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