It has occurred to me since May 2015 that for certain purposes the matter term in the Friedman equation might benefit from a modification. https://www.physicsforums.com/threads/how-does-a-particles-kinetic-energy-vary-with-a-t.811627The Friedmann equation shows the matter term to be based on the assumption that the particles of matter never acquires any significant kinetic energy. One example for which this assumption is inadequate is calculating the affect on the solution t(a) by assuming DM consists of particles with small mass. In 1998 the idea that neutrinos might be the stuff of DM was an active possibility. http://www.astro.ucla.edu/~wright/neutrinos.htmlApparently it is still active at MIT. http://web.mit.edu/lns/research/neutrino.html http://www2.lns.mit.edu/neutrino/dark_matter.htmlHowever, I have been unable to find any articles discussing the effect on t(a) based on modifying the mass term, even though the corresponding change in t(a) could have a significant impart on the primordial nucleosynthesis of deuterium. https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis#DeuteriumTo evaluate this possibility, the first step would seem to be to find the appropriate revised function F(a) to replace F(a) = a-3as the coefficient of ΩM. I would much appreciate if one or more participants of PF would check my math and post descriptions of any errors they find, or to acknowledge that they found none. The mass term in the Friedmann equation that I derived is: It is clear that for a = ε << 1: Q02 << 1, and F(a) ≈ a-3. Also, for 1-a = e << 1: Q02 ≈ 1, and F(a) ≈ a-4. The following is the derivation of the modified F(a).