We show that Fermi repulsion can lead to cored density profiles in dwarf galaxies for sub-keV fermionic dark matter .
We treat the dark matter as a quasi-degenerate self-gravitating Fermi gas and calculate its density profile assuming hydrostatic equilibrium .
We find that suitable dwarf galaxy cores of size \gtrsim 130 pc can be achieved for fermion dark matter with mass in the range 70 eV – 400 eV .
While in conventional dark matter scenarios , such sub-keV thermal dark matter would be excluded by free streaming bounds , the constraints are ameliorated in models with dark matter at lower temperature than conventional thermal scenarios , such as the Flooded Dark Matter model that we have previously considered .
Modifying the arguments of Tremaine and Gunn we derive a conservative lower bound on the mass of fermionic dark matter of 70 eV and a stronger lower bound from Lyman \alpha clouds of about 470 eV , leading to slightly smaller cores than have been observed .
We comment on this result and how the tension is relaxed in dark matter scenarios with non-thermal momentum distributions .