DBI Softens Stiff-Phase Gravitational-Wave Spectra

We investigate the effect of non-canonical kinetic terms on the present-day density spectrum of primordial gravitational waves (GWs), by considering the dynamics of a scalar field governed by the Dirac--Born--Infeld (DBI) action and a runaway potential. The field, responsible for a period of inflation, subsequently enters a kinetically dominated regime, where the DBI structure reduces the equation-of-state parameter relative to the canonical kination result $w=1$, thereby softening the blue tilt of the GW spectrum. Simultaneously, the energy density of the field redshifts at a slower rate, delaying radiation domination and prolonging the stiff phase. The interplay between these two effects can lead to a potentially observable GW signal that would otherwise remain beyond the reach of future experiments in the canonical case. We test our predictions by numerically solving the background and perturbations, from inflation until radiation domination, and find viable parameter space compatible with cosmic microwave background and Big Bang Nucleosynthesis constraints.