Monopoles Without Inflation: The Relic Abundance Implied by a Finite Maximum Temperature

This paper computes a consequence of the torsion-regulated bounce for topological defects, using the density ceiling of 9.718e+54 grams per cubic centimetre and the maximum temperature of 3.278e+22 kelvin that follows from it. At the ceiling the horizon volume contains, on the stated counting, a monopole density of 4.701e+46 per cubic metre, against an entropy density of 1.373e+77 per cubic metre in units of Boltzmann's constant. The yield is therefore Y = 3.423e-31 monopoles per unit entropy. With a monopole mass of 3.486e+11 GeV per c squared, that is 6.215e-16 kilograms, the frozen yield corresponds to a present density parameter Omega = 3.275e-11. That is far below unity: monopoles at the maximum abundance this cosmology permits would be a negligible fraction of the present energy budget, and the corresponding isotropic flux proxy, 2.361e-14 per square metre per steradian per second, sits comfortably below the classic Parker bound level. The monopole problem, in its density form, does not arise here, not because an expansion diluted the monopoles, but because the finite maximum temperature kept their birth yield small. The calculation is performed from stated assumptions with all arithmetic deposited, and it is a computation, not a measurement.