Flat Friedmann Universe Filled by Dust and Scalar Field with Multiple Exponential Potential

We study a spatially flat Friedmann model containing a pressureless perfect fluid (dust) and a scalar field with an unbounded from below potential of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$V(\varphi ) = W_0 - V_0 {\text{ sinh(}}\sqrt {{\text{3/2}}} \kappa \varphi {\text{)}}$$ \end{document}, where the parameters W0 and V0 are arbitrary and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\kappa = \sqrt {{8\pi }G_N } = M_p^{ - 1} $$ \end{document}. The model is integrable and all exact solutions describe the recollapsing universe. The behavior of the model near both initial and final points of evolution is analyzed. The model is consistent with the observational parameters. We single out the exact solution with the present-day values of acceleration parameter q0=0.5 and dark matter density parameter Ωρ0=0.3 describing the evolution within the time approximately equal to 2H0−1.