Einstein's Equations and a Cosmology with Finite Matter
  We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta function at the time of the big bang thereafter diffusing outward with constant total mass. This proposal explores a departure from standard assumptions that the big bang occurred everywhere at once or was just one of an infinite number of previous and later transitions. 
L. Clavelli and Gary R. Goldstein
gr-qc astro-ph.CO hep-th