The Shift of the Scalar Spectral Index Produced by a Torsion-Dominated Phase: Magnitude Against the Planck Uncertainty

The shift reaches the Planck uncertainty at a density ratio of only r = 4.196e-03: a mode exiting the horizon when the density is a few parts in a thousand of the bounce density already carries, in this model, a tilt displacement of one standard deviation. At r = 0.01 the shift is 0.0100; at r = 0.1 it is 0.1026; at r = 0.5 it is 0.5858, which is 139.5 times the Planck uncertainty of 0.0042. The growth is concave, following the square-root form, so most of the displacement accumulates surprisingly early in the approach to the bounce density. Modes that exit deep in the torsion-modified regime would bear tilts displaced far beyond observational tolerance, which converts the Planck measurement into a bound: the modes we actually observe cannot have exited at large density ratios in a phase described by this model. The study is a computation from stated assumptions, performed by the accompanying script; it is simulated, not measured.