An Effective Sign Switching Dark Energy: Lotka-Volterra Model of Two Interacting Fluids

One of the recent attempts to address the Hubble and $S_8$ tensions is to consider the Universe started out not as a de Sitter-like spacetime, but rather anti-de Sitter-like. That is, the Universe underwent an "AdS-to-dS" transition at some point. We study the possibility that there are two dark energy fluids, one of which gave rise to the anti-de Sitter-like early Universe. The interaction is modeled by the Lotka-Volterra equations, commonly used in population biology. We consider "competition" models that are further classified as "unfair competition" and "fair competition". The former involves a quintessence in competition with a phantom, and the second involves two phantom fluids. Surprisingly, even in the latter scenario it is possible for the overall dark energy to cross the phantom divide. The latter model also allows a constant $w$ "AdS-to-dS" transition, thus evading the theorem that such a dark energy must possess a singular equation of state. We also consider a "conversion" model in which a phantom fluid still manages to achieve "AdS-to-dS" transition even if it is being converted into a negative energy density quintessence. In these models, the energy density of the late time effective dark energy is related to the coefficient of the quadratic self-interaction term of the fluids, which is analogous to the resource capacity in population biology.