Oscillatory Features in the Primordial Spectrum From the Phase Accumulated Through a Bounce

A bounce imprints a phase on every perturbation mode that passes through it, and a phase that varies with wavenumber appears in the power spectrum as an oscillation. This paper computes the amplitude and frequency of that ringing for a torsion-regulated bounce and states the size of the signal that feature searches should look for. The spectrum carries a modulation 1 + A sin(omega ln(k/k*) + phi) with amplitude A(omega) = 0.045 exp(-omega/38). At the fiducial frequency omega = 32 the amplitude is 0.01939, a maximum fractional deviation of 1.9 percent from the smooth spectrum, with 35 oscillation cycles across the observable wavenumber interval and a root-mean-square deviation of 1.4 percent. At low frequency the amplitude rises to 0.0346, while by omega = 80 it has fallen to 0.005482. Planck feature searches constrain modulations of this logarithmic type to the level of a few percent over much of this frequency range, so the prediction lies within reach of existing analyses at low frequency and below them at high frequency. The study is computed from stated assumptions, not measured.