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We examine the backreaction effect of the enhanced small-scale scalarperturbations from the sound speed resonance (SSR) mechanism for primordialblack hole formation in Dirac-Born-Infeld (DBI) inflation on background as wellas curvature perturbation, which can generate a considerable amount ofprimordial black holes (PBH) in the radiation-dominated epoch. Within theperturbative regime, the backreaction effect of perturbations on the backgrounddynamics can be described by an effective action after integrating out theperturbation sector. Starting with the effective field theory of a specific DBIinflation model that incorporates SSR, we obtain the one-loop effective actionby integrating out the scalar perturbations at the quadratic level. Using theeffective Friedmann equations derived from this one-loop effective action, wesolve the Hubble parameter with backreaction and the effective perturbationdynamics on this background as well. Our numerical findings reveal that, for aviable parameter space, the backreaction effect results in a relativecorrection to the Hubble parameter of approximately $10^{-7}$, whereas therelative correction to the slow-roll parameter can vary between $-0.3$ and$0.1$, before gradually converging to $10^{-7}$. Furthermore, our results showthat the backreaction effect on SSR sound speed causes a slight reduction inthe resonant peak of the curvature power spectrum, and the subsequent PBHformation predicted by the SSR mechanism remains almost unchanged.

The backreaction effect of the sound speed resonance in DBI inflation