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The Dvali-Gabadadze-Porrati model introduces a parameter, the cross-overscale $r_c$, setting the scale where higher dimensional effects are important.In order to agree with observations and to explain the current acceleration ofthe Universe, $r_c$ must be of the order of the present Hubble radius. Wediscuss a mechanism to generate a large $r_c$, assuming that it is determinedby a dynamical field and exploiting the quantum effects of the graviton. Forsimplicity, we consider a scalar field $\Psi$ with a kinetic term on the braneinstead of the full metric perturbations. We compute the Green function and the1-loop expectation value of the stress tensor of $\Psi$ on the backgrounddefined by a flat bulk and an inflating brane (self-accelerated or not). Wealso include the flat brane limit. The quantum fluctuations of the bulk field$\Psi$ provide an effective potential for $r_c$. For a flat brane, the 1-loopeffective potential is of the Coleman-Weinberg form, and admits a minimum forlarge $r_c$ without fine tuning. When we take into account the brane curvature,a sizeable contribution at the classical level changes this picture and thepotential develops a (minimum) maximum for the (non-) self-accelerated branch.Comment: 16 pages, 2 figures. References adde

Quantum fluctuations in the Dvali–Gabadadze–Porrati model and the size of the crossover scale