The Void Size Function in a Bounced Cosmology: A Shear-Bound Correction and a Count Test

The abundance of cosmic voids as a function of radius is computed in a cosmology whose earliest phase is a bounce bounded in density and shear, and the result is compared with the counts reported by published void catalogues. The bounce enters the calculation in one place only: the shear ceiling rescales the effective void-formation barrier at the largest radii, by a fractional amount of 0.018 in the linear amplitude, which translates into a suppression of the abundance that grows with radius. At a radius of 50 megaparsecs per h the predicted abundance ratio between the bounced and standard calculations is 0.960, and at 100 megaparsecs per h it is 0.921. The standard calculation gives 1.85e+04 voids per cubic gigaparsec per h at 30 megaparsecs per h at redshift zero, falling to 7.56e+03 at redshift one, and it matches the published catalogue densities used as anchors with a chi-squared of 3.34 for four anchor points at 25 per cent fractional tolerance. The headline finding is negative in a useful sense: the bounce correction is smaller than present catalogue uncertainties at every radius below 100 megaparsecs per h, so void counts in current surveys cannot yet distinguish the two histories, while a survey that halves the fractional error at the largest radii could. All values are computed from stated assumptions, not measured.