Bouncing cosmology from nonlinear dark energy with two cosmological constants

We explore the dynamics of Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies which consist of dark matter, radiation, and dark energy with a quadratic equation of state. Standard cosmological singularities arise due to energy conditions which are violated by dark energy, therefore we focus our analysis on nonsingular bouncing and cyclic cosmologies, in particular focusing on the possibility of closed FLRW models always having a bounce for any initial conditions. We analyze the range of dynamical behavior admitted by the system, and find a class of closed models that admit a nonsingular bounce, with early- and late-time accelerated expansion connected by a decelerating phase. In all cases, we find the bouncing models are only relevant when dark matter and radiation appear at a certain energy scale, and so require a period such as reheating. We then investigate imposing an upper bound on the dark matter and radiation, such that their energy densities cannot become infinite. In this case, we find that all closed models bounce, and a class of models exist with early- and late-time acceleration, connected by a decelerating phase. We also consider parameter values for the dark energy component, such that the discrepancy between the observed value of Λ and the theoretical estimates of the contributions to the effective cosmological constant expected from quantum field theory would be explained. However, we find that the class of models left does not allow for an early- and late-time accelerated expansion, connected by a decelerating period where large-scale structure could form. Nonetheless, our qualitative analysis serves as a basis for the construction of more realistic models with realistic quantitative behavior.