Suppression of Large-Scale Scalar Power by the Bounce Scale: Quadrupole and Low-Multipole Consequences

Modes much larger than the bounce horizon scale are not transmitted through a bounce perfectly; part of their amplitude is reflected by the rapid transition. This paper computes the resulting suppression of the primordial power spectrum at large scales and its consequences for the lowest microwave multipoles. With a bounce scale k_b = 1.6e-3 per megaparsec, the transmitted power ratio is 0.461 at the quadrupole scale, 0.885 at k = 0.002 per megaparsec, and 1 at the pivot scale, so the suppression is confined to the largest scales. The power-weighted average ratio over the low-wavenumber band is 0.861. The predicted deficit at the low-multipole scale, 0.115 of the unsuppressed power, is larger than the mild deficit the Planck data suggest at low multipoles, and requiring the ratio at k = 0.002 to exceed 0.80 already bounds the bounce scale above at k_b = 0.001988 per megaparsec in the conventions used here, a bound the fiducial value satisfies only marginally. The low-multipole sky thus constrains the bounce scale from a direction independent of the tilt and the non-Gaussianity channels. The study is computed from stated assumptions, not measured.