Nonlinear electrodynamics and modification of initial singularities, and dark matter and dark energy affecting structure formation in the early and later universe

We find that having the scale factor close to zero due to a given magnetic field value in an early universe magnetic field affects how we would interpret Mukhanov's chapter on "self reproduction" of the universe in in his reference. The stronger an early-universe magnetic field is, the greater the likelihood of production of about 20 new domains of size 1/H, with H the early-universe Hubble constant, per Planck time interval in evolution. We form DM from considerations as to a minimum time step, and then generate DM via axions. Through Ng's quantum infinite statistics, we compare a DM count, giving entropy. The remainder of the document is in terms of DE as well as comparing entropy in galaxies versus entropy in the universe, through a lens of Mistra's quantum theory of the big bang. (paper)