Primordial Tensor Spectral Index of a Torsion Bounce: A Computed Blue Tilt and Its Amplitude Cost

This study computes a specific gravitational-wave consequence of a torsion-regulated bounce in Einstein-Cartan gravity, taking the limiting density for neutron matter, 9.72e+54 grams per cubic centimetre under the stated prescription, as its single input scale. A blue tensor tilt is often quoted as a generic bounce signature; the calculation here shows the tilt is fixed by the contraction rate, that a matter-like contraction gives an exactly scale-invariant tensor spectrum in this treatment, and that stiffer contraction buys its blue tilt at an amplitude cost at small scales so steep that the tilt and the large-scale amplitude cannot both be large. The headline results of the computation are: n_T_fiducial = 2.00, growth = 9.79e+17, A_t_pivot = 7.56e-11, A_t_smallscale_power = 7.25e+25, w_fiducial = 0.333, n_T_matter_contraction = 0.00, r_max_if_blue = 4.96e-40. Each quantity is evaluated by the deposited script from the assumptions stated in the Methods, and the agreement or disagreement of each quantity with published observational bounds is reported at face value, including where the conclusion is that the channel examined is closed. The study is simulated and computed from stated assumptions; it is not a measurement, and no observational data were taken for it.