In this work, we constrain the value of ${\sigma }_8$ for the normal and self-accelerating branch of a Dvali-Gabadadze-Porrati brane embedded in a five-dimensional Minkowski space-time. For that purpose, we first constrain the background model parameters $H_0$, ${\mathrm{\Omega }}_{m0}$, ${\mathrm{\Omega }}_{r0}$, and $M$ using the $\mathrm{Pantheon}+\text{catalog}$ and a mock catalog of gravitational waves. Then, we numerically solve the equation for dark matter scalar perturbations using the dynamic scaling solution for the master equation. Finally, we found that the evolution of matter density perturbations in both branches is different from the $\mathrm{\Lambda }\mathrm{CDM}$ model and that the value of ${\sigma }_8=0.774\pm 0.027$ for the normal branch and ${\sigma }_8=0.913\pm 0.032$ for the self-accelerating branch.

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• Alternative gravity theories
• Cosmological parameters
• Gravitational waves
• Gravity in dimensions other than four
• Large scale structure of the Universe