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

Abstract

Abstract. 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 V (ϕ) = W 0 − V 0 sinh 3/2κϕ , where the parameters W 0 and V 0 are arbitraryThe 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 q 0 = 0.5 and dark matter density parameter Ω ρ0 = 0.3 describing the evolution within the time approximately equal to 2H −1 0 .

Negative potentials and collapsing universes

“…We will also assume that the function Q(φ), that is the logarithmic derivative of the dilaton χ(φ), is bounded for all φ ∈ R: in particular, we will suppose the existence of a constant A such that (6) 4…”

Dynamical systems approach in scalar field cosmologies

“…This result generalises previous investigations indicating that negative potentials may drive a flat initially expanding Universe to recollapse, see [104][105][106].…”

“…We firstly analyse the case E when the scalar field negatively diverges in such a way that V (φ(t)) → +∞, see for example [106]. Note that we do not need to assume an a priori estimate on α, β.…”

Negative potentials and collapsing universes II

“…Case φ ∞ = −∞. We firstly analyse the case C when the scalar field negatively diverges in such a way that V (φ(t)) → +∞, see for example [7]. We use expansion normalized variables techniques, first introduced in [26]; see also [15,12].…”

“…(see [7] where an exact solution was obtained in the absence of matter). D. Potentials having a global positive maximum and lim φ→±∞ V (φ) = −∞.…”