Diluting Cosmological Constant via Large Distance Modification of   Gravity
  We review a solution of the cosmological constant problem in a brane-world model with infinite-volume extra dimensions. The solution is based on a nonlinear generally covariant theory of a metastable graviton that leads to a large-distance modification of gravity.   From the extra-dimensional standpoint the problem is solved due to the fact that the four-dimensional vacuum energy curves mostly the extra space. The four-dimensional curvature is small, being inversely proportional to a positive power of the vacuum energy. The effects of infinite-volume extra dimensions are seen by a brane-world observer as nonlocal operators.   From the four-dimensional perspective the problem is solved because the zero-mode graviton is extremely weakly coupled to localized four-dimensional sources. The observable gravity is mediated not by zero mode but, instead, by a metastable graviton with a lifetime of the order of the present-day Hubble scale. Therefore, laws of gravity are modified in the infrared above the Hubble scale. Large wave-length sources, such as the vacuum energy, feel only the zero-mode interaction and, as a result, curve space very mildly. Shorter wave-length sources interact predominantly via exchange of the metastable graviton. Because of this, all standard properties of early cosmology, including inflation, are intact. 
Gia Dvali, Gregory Gabadadze, M. Shifman