Gravitational constraints of dS branes in AdS Einstein-Brans-Dicke bulk

We derive the full projected Einstein-Brans-Dicke gravitational equations associated with a n-dimensional brane embedded in a (n+1)-dimensional bulk. By making use of general conditions, as the positivity of the Brans-Dicke parameter and the effective Newton gravitational constant as well, we are able to constrain the brane cosmological constant in terms of the brane tension, the Brans-Dicke scalar field, and the trace of the stress tensor on the brane, in order to achieve a $dS$ brane. Applying these constraints to a specific five-dimensional model, a lower bound for the scalar field on the brane is elicited without solving the full equations. It is shown under which conditions the brane effective cosmological constant can be ignored in the brane projected gravitational field equations, suggesting a different fine tuning between the brane tension and the bulk cosmological.