  Einstenian cubic gravity (ECG) is a modified theory of gravity constructed
with cubic contractions of the curvature tensor. This theory has the remarkable
feature of having the same two propagating degrees of freedom of Einstein
gravity (EG), at the perturbative level on maximally symmetric spacetimes. The
additional unstable modes steaming from the higher order derivative dynamics
are suppressed provided that we consider the ECG as an effective field theory
wherein the cubic terms are seen as perturbative corrections of the
Einstein-Hilbert term. Extensions of ECG have been proposed in cosmology and
compact objects in order to probe if this property holds in more general
configurations. In this work, we construct a modified ECG gravity in a five
dimensional warped braneworld scenario. By assuming a specific combination of
the cubic parameters, we obtained modified gravity equations of motion with
terms up to second-order. For a thin 3-brane, the cubic-gravity corrections
yield an effective positive bulk cosmological constant. Thus, in order to keep
the 5D bulk warped compact, an upper bound of the cubic parameter with respect
to the bulk curvature was imposed. For a thick brane, the cubic-gravity terms
modify the scalar field potential and its corresponding vacuum. Nonetheless,
the domain-wall structure with a localized source is preserved. At the
perturbative level, the Kaluza-Klein (KK) tensor gravitational modes are stable
and possess a localized massless mode provided the cubic corrections are small
compared to the EG braneworld.
