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.

References

Primordial black hole formation in matter-domination is, however, presently plagued with some uncertainty given the number of effects that become relevant in the absence of ambient pressure (e.g.~angular momentum, anisotropic collapse). We will therefore leave a detailed analysis of the effects of the early-matter era for a future dedicated work.

— Lukewarm inflation and the QCD axion  (2609.19284 - Ferraz et al., 16 Sep 2026) in Section 4.2, subsection “Enhancement of small-scale curvature perturbations”

As the next steps, we need to include non-relativistic matter into the model and check if the transition to a matter-dominated cosmology could be successfully achieved.

— Vacuum energy problem in anti-de Sitter space  (2608.25860 - Arbuzova et al., 26 Aug 2026) in Section Conclusion