Cosmology of fermionic dark matter

We explore a model for a fermionic dark matter particle family which decouples from the rest of the particles when at least all standard model particles are in equilibrium. We calculate the allowed ranges for mass and chemical potential to be compatible with big bang nucleosynthesis (BBN) calculations and WMAP data for a flat universe with dark energy (Omega(0)(Lambda)=0.72, Omega(0)(M)=0.27, h=0.7). Futhermore we estimate the free streaming length for fermions and antifermions to allow comparison to large scale structure data (LSS). We find that for dark matter decoupling when all standard model particles are present even the least restrictive combined BBN calculation and WMAP results allow us to constrain the initial dark matter chemical potential to a highest value of 6.3 times the dark matter temperature. In this case, the resulting mass range is at most 1.8 eV <= m <= 53 eV, where the upper bound scales linearly with g(eff)(s)(T-Dec). From LSS we find that, similar to ordinary warm dark matter models, the particle mass has to be larger than similar to 500 eV [meaning g(eff)(s)(T-Dec)> 10(3)] to be compatible with observations of the Ly alpha forest at high redshift, but still the dark matter chemical potential over temperature ratio can exceed unity.