Adiabatic Compression Through a Bounce: Tracing a Present-Day Nanogauss Field Back to the Turnaround

A magnetic field frozen into a highly conducting plasma strengthens as the inverse square of the scale factor during contraction and weakens by the same law during expansion. This paper follows that simple law through a cosmology that contracts to a maximum density of 9.72e+57 kg per cubic metre and turns around, instead of beginning at a singularity. Tracing a present-day field of 1 nanogauss backwards gives a field at the turnaround of 1.45e+31 tesla, or 1.45e+35 gauss, yet its energy density there is only a fraction 9.53e-08 of the total density at the turnaround, because the background density rises with the same fourth power of the inverse scale factor. Even the largest field allowed by cosmic microwave background limits, 4.4 nanogauss today, corresponds to a fraction of only 1.85e-06 at the turnaround. Adiabatic compression through a bounce is therefore energetically cheap: it neither requires nor produces anything close to equipartition, and any claim that a present nanogauss field must have dominated the bounce is arithmetically false. The calculation is simulated from stated assumptions, not measured.