Distribution of Matter from Singularity with Spherical Symmetry Using   Fick Diffusion
  A model is presented allowing calculation of energy and matter distribution in the Universe after expansion from singularity without introduction of expansion energy. Beginning with Fick's law of diffusion, we solve the Bessel function for spherical systems during expansion, presuming isotropic matter distribution in the Hubble flow. This function can be substituted with the Associated Legendre differential equation and when solved we discover useful parameters for those of energy and matter densities, diffusion and temperature. Though we can follow the decline of matter density over spacetime, we cannot suggest a precise value at singularity. This model may be useful though, as a starting point for modeling star formation rates, SFR, galaxy formation horizon lengths and regions devoid of matter where tracing the matter density decline over time is important. 
Ahmet Mecit \"Ozta\c{s} and Michael L. Smith