Kensuke Sueto, Riku Yoshimoto, Pablo A. Cano

We study braneworld cosmology in quasi-topological gravity (QTG) with an infinite tower of higher-curvature terms, focusing on the case in which the bulk admits regular black hole solutions. We derive the $\mathbb{Z}_2$-symmetric junction conditions for a FLRW brane moving in a static, spherically symmetric bulk geometry, and obtain the corresponding modified Friedmann equations for the scale factor. We prove that, in the small scale factor regime, the brane generically approaches a de Sitter phase characterized solely by the length scale $\sqrtα$ of the higher-derivative terms, while the standard Einstein-gravity braneworld dynamics is recovered in the low-energy regime. We further provide a universal estimate for the number of e-folds of the de Sitter phase in terms of the ratio between the black hole scale and the scale of new physics $r_g/\sqrtα$. The inflationary regime is fully independent of the brane matter content and hence avoids the problem of trans-Planckian matter densities. Numerical integrations for explicit regular bulk solutions (Dymnikova-like and Hayward black holes) confirm these estimates and illustrate how the bulk black hole sector controls the onset and termination of inflation. This framework leverages the powerful properties of QTGs, defined only in $D\ge 5$, to study consequences for a four-dimensional universe.