The Matter Power Spectrum Turnover in a Bounced Cosmology: Equality Scale Against a Bounce Scale

The matter power spectrum turns over at the scale that entered the horizon at matter-radiation equality, near a hundredth of a reciprocal megaparsec. The equality scale comes out at 0.010 per megaparsec. A cutoff at 0.1 per megaparsec would suppress power at 0.05 per megaparsec by 22.12 percent, which surveys would not have missed; a cutoff at 0.5 per megaparsec suppresses the same point by only 1.0 percent. Requiring the distortion to stay below roughly two percent places the bounce wavenumber above about 0.30 per megaparsec, corresponding to a bounce horizon smaller than a few megaparsecs in comoving terms, comfortably consistent with, and weaker than, the small-scale variance bound but derived from an entirely different observable. Computed from stated assumptions, not measured.