Photon Diffusion Damping with a Modified Pre-Recombination History: A Bound from the Damping Tail

Before recombination, photons diffused out of small-scale fluctuations, erasing them. A residual expansion change of one percent at recombination would move the damping wavenumber from 0.140 to 0.1407 per megaparsec, a shift of 0.5 percent, at the edge of present precision. The damping tail therefore limits any residual effect to about 2.0 percent. Propagated back through the sixth-power scaling of the spin density, even this modest limit excludes a bounce occurring as late as the epoch the damping integral weights most heavily, though it does not compete with the nucleosynthesis bounds for an early bounce, a hierarchy this paper states openly. Computed from stated assumptions, not measured.