2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98981Primordial gravitational waves are amplified during eras when their wavelengths are pushed outside the cosmological horizon. This occurs in both inflationary and ``pre-big-bang'' or ``bounce'' cosmologies. The spectrum is expressed as a normalized energy density per unit logarithmic frequency, denoted Omega. The spectral index (logarithmic slope) of Omega is simply related to three properties of the early universe: (i) the gravitons' mean initial quantum occupation number N(n) (=1/2 for a vacuum state), where n is the (invariant) conformal frequency of the mode, and (ii) & (iii) the parameter gamma=p/rho of the cosmological equation of state during the epoch when the waves left the horizon (gamma=gamma_i) and when they reentered (gamma=gamma_f). In the case of an inflationary cosmology, the spectral index is equal to d(ln N)/d(ln n) + 2(gamma_i + 1)/(gamma_i + 1/3) + 2(gamma_f - 1/3)/(gamma_f + 1/3) and for bounce cosmologies it is equal to d(ln N)/d(ln n) + 4(gamma_i)/(gamma_i + 1/3) + 2(gamma_f - 1/3)/(gamma_f + 1/3) These expressions are compared against various more model-specific results given in the literature.5 pages REVTeX, 3 figuresGeneral Relativity and Quantum Cosmologytext