Growth of Structure with a Bounce-Imposed Initial Cutoff: The Suppression of the Linear Growth Factor

Structure grows from initial fluctuations, and a bounce changes the initial conditions in one specific way: fluctuations on scales smaller than the bounce horizon at the turnaround cannot have been laid down causally in the contracting phase in the usual manner, so the initial spectrum carries a cutoff at a characteristic wavenumber. For a cutoff at 1 per megaparsec the variance on the integrated galaxy-scale band falls by 43.46 percent, an effect far larger than current uncertainties and therefore already excluded; at 10 per megaparsec the loss is 0.6 percent, and at 50 per megaparsec it is 0.02 percent, below present sensitivity. The growth factor itself, reaching 0.608 of its present value by redshift one, is unchanged in shape: the bounce alters the initial spectrum, not the subsequent growing mode, within this treatment. Computed from stated assumptions, not measured.