Tremaine-Gunn Control: Evading Bounds on Light Fermion Dark Matter

Abstract

Pauli exclusion is often regarded as imposing a model-independent lower bound on the mass of fermionic dark matter in galaxies. We show that dark-sector interactions can substantially weaken this conclusion. In particular, eV-scale fermions can form bound structures with the characteristic sizes and densities of dwarf galaxies, thereby circumventing the conventional Tremaine-Gunn mass constraint. Within these objects, the degeneracy pressure is balanced by an attractive finite-range scalar Yukawa force that is significantly stronger than gravity. The interaction acts on dwarf-galaxy scales while remaining screened on larger scales. We derive the evolution of the resulting dark-matter fluid and identify a viable cosmological history in which structures first form gravitationally, with the new interaction becoming active only at late times. As a proof of concept, we construct a model in which a single late-time phase transition generates the required dynamics. These results provide a new route to exceptionally light fermionic dark matter and demonstrate that dark-sector interactions can qualitatively alter conventional phase-space limits.