Cosmological constant problem and brane world

We present a framework to address the cosmological constant problem in which gravity is allowed to propagate in infinite volume extra dimensions while the Standard Model fields are localized on a lower dimensional hypersurface (brane).; First, we study gravity in codimension-2 brane world scenarios with infinite volume extra dimensions. In particular, we consider the case where the brane has non-zero tension. We study (linearized) gravity in the presence of the Einstein-Hilbert term on the brane in such backgrounds. We find that gravity is almost completely localized on the brane with ultra-light modes penetrating into the bulk.; Then, we discuss some issues arising in studying (linearized) gravity on non-BPS higher codimension branes in an infinite-volume bulk. In particular, such backgrounds are badly singular for codi-mension-3 and higher delta-function-like branes with non-zero tension and we discuss that adding higher curvature terms might be necessary in this context. We then discuss the cosmological constant problem in this context. In particular, by adding higher curvature terms in the bulk action we are able to find smooth solutions with the property that the 4-dimensional part of the brane world-volume is flat for a range of positive values of the brane tension.