A Ceiling on Cosmic String Tension from the Torsion-Regulated Bounce

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. The ceiling density is 9.718e+54 grams per cubic centimetre, reached at a maximum temperature of 3.278e+22 kelvin, or 2.825e+09 GeV in thermal units. The largest symmetry scale a hot-phase transition can reach is therefore eta = 2.544e+09 GeV. The corresponding tension is mu = 5.847e+07 kilograms per metre, which is G mu = 4.342e-20. The deficit angle around such a string is 1.091e-18 radians, or 2.251e-13 arcseconds. Set against the published bounds, the ceiling sits a factor 3.340e-13 of the microwave-background limit of 1.3 x 10^-7 and a factor 4.342e-10 of the representative pulsar-timing level of 10^-10. Inverting the observational bounds through the same formulae, the microwave limit corresponds to a symmetry scale of 4.402e+15 GeV and the pulsar-timing level to 1.221e+14 GeV: both lie far above the ceiling scale, by factors of 1.730e+06 and 4.799e+04 respectively in eta. Changing the prescription coefficient to C = 1/2 lowers the ceiling scale only to 1.799e+09 GeV, because of the fourth-root dependence. The calculation is performed from stated assumptions with all arithmetic deposited, and it is a computation, not a measurement.