Late time evolution of negatively curved FLRW models

Understand

We study the late time evolution of negatively curved Friedmann--Le\-ma\^{\i}tre--Robert\-son--Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter.

• Since, under mild assumptions on the potential $V$, it is already known that equilibria corresponding to non-negative local minima for $V$ are asymptotically stable, we classify all cases where one of the energy components eventually dominates.
• In particular for nondegenerate minima with zero critical value, we rigorously prove that if $\gamma$, the parameter of the equation of state is larger than $2/3$, then there is a transfer of energy from the fluid and the scalar field to the energy density of the scalar curvature.
• Thus, the scalar curvature, if present, has a dominant effect on the late evolution of the universe and eventually dominates over both the perfect fluid and the scalar field.