Can Compactifications Solve the Cosmological Constant Problem?

Recently, there have been claims in the literature that the cosmological constant problem can be dynamically solved by specific compactifications of gravity from higher-dimensional toy models. These models have the novel feature that in the four-dimensional theory, the cosmological constant $\Lambda$ is much smaller than the Planck density and in fact accumulates at $\Lambda=0$. Here we show that while these are very interesting models, they do not properly address the real cosmological constant problem. As we explain, the real problem is not simply to obtain $\Lambda$ that is small in Planck units in a toy model, but to explain why $\Lambda$ is much smaller than other mass scales (and combinations of scales) in the theory. Instead, in these toy models, all other particle mass scales have been either removed or sent to zero, thus ignoring the real problem. To this end, we provide a general argument that the included moduli masses are generically of order Hubble, so sending them to zero trivially sends the cosmological constant to zero. We also show that the fundamental Planck mass is being sent to zero, and so the central problem is trivially avoided by removing high energy physics altogether. On the other hand, by including various large mass scales from particle physics with a high fundamental Planck mass, one is faced with a real problem, whose only known solution involves accidental cancellations in a landscape.