Matter inclusion and transition to matter domination

Determine whether incorporating non-relativistic matter into the scalar-field curvature-compensation model can successfully produce a transition to a matter-dominated cosmology.

Background

The paper studies a scalar field non-minimally coupled to the curvature scalar as a mechanism for dynamically neutralizing the gravitational effect of a large negative vacuum energy in anti-de Sitter space. Its numerical and analytical results lead instead to an asymptotic radiation-like expansion with Hubble parameter proportional to the inverse of time. The authors identify the inclusion of non-relativistic matter and the resulting transition to matter domination as an unresolved next step, since the analysis assumes relativistic matter whose energy-momentum trace vanishes.