Self-tuning of the cosmological constant in brane-worlds with $P(X,φ)$

Abstract: We revisit the idea of self-tuning the observed cosmological constant to a vanishing value and promote it to a selection criterion of brane-world models, in which our Universe is described by a 3-brane embedded in a 5d bulk. As a concrete setup, we consider a bulk scalar field $\phi$ described by a general Lagrangian $P(X,\phi)$ with $X=-(\partial\phi)<sup>2/2$. By requiring that the model enforces the 4d curvature of the maximally symmetric 3-brane world-volume to vanish independently of the 4d effective vacuum energy, only two possibilities remain: one with a canonical bulk kinetic term and the other with an unconventional bulk kinetic term similar to a Cuscuton field. Further demanding the absence of bulk singularity, the latter is selected as a unique possibility within the class of models. At the background level, the solution can accommodate any warp factor profile free from bulk singularity and with a finite effective 4d Planck mass. In a cosmological context, our solution would describe our (almost) flat Universe at late times, with a bulk warp factor profile expected to be determined by the evolution of the Universe before dilution of the matter fields by cosmic expansion. Eventually, a simple analysis is performed in the bulk showing no obvious instability around the background solution. A full stability analysis taking into account brane bending modes is nevertheless necessary and left for future work.