2-component cosmological models with perfect fluid and scalar field: Exact solutions

We study integrability by quadrature of a spatially flat Friedmann model containing both a perfect fluid with barotropic equation of state rho = (1 - h)rho and a minimally coupled scalar field p with either a single exponential potential V(phi) similar to exp[-root6sigmakappaphi], kappa = root8piG(N), of arbitrary sign or a, simplest multiple exponential potential V ( phi) = W-0 - V-0 sinh (root6sigmakappaphi), where the parameters W-0 and V-0 are arbitrary. 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 a and h. For the single exponential potential we present 4 classes of general solutions with the parameters obeying the following relations: A. sigma is arbitrary, h = 0; B. sigma = 1 - h/2, 0 < h < 2; C1. sigma = 1 - h/4, 0 < h less than or equal to 2; C2. sigma - \1-h\, 0 < h less than or equal to 2, h not equal1,4/3. The properties of the exact solutions near the initial singularity and at the final stage of evolution are analyzed. For the multiple exponential potential the model is integrated with h = 1 and sigma = 1/2 and all exact solutions describe the recollapsing universe. We single out the exact solution describing the evolution within the time approximately equal to 2H(0)(-1) with the present-day values of the acceleration parameter q(0) = 0.5 and the density parameter Omega(rho0) = 0.3.