Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-12-26
Grav.Cosmol. 9 (2003) 189-195
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages, Latex, 1 figure, submit. to Class. Quantum Grav
Scientific paper
We study integrability by quadrature of a spatially flat Friedmann model containing both a minimally coupled scalar field $\phi$ with an exponential potential $V(\phi)\sim\exp[-\sqrt{6}\sigma\kappa\phi]$, $\kappa=\sqrt{8\pi G_N}$, of arbitrary sign and a perfect fluid with barotropic equation of state $p=(1-h)\rho$. 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 $\sigma$ 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}. $\sigma$ is arbitrary, $h=0$; {\bf B}. $\sigma=1-h/2$, $0
Dehnen Heinz
Gavrilov V. R.
Melnikov Vitaly N.
No associations
LandOfFree
General solutions for flat Friedmann universe filled by perfect fluid and scalar field with exponential potential does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with General solutions for flat Friedmann universe filled by perfect fluid and scalar field with exponential potential, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General solutions for flat Friedmann universe filled by perfect fluid and scalar field with exponential potential will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-604974