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.
