Can Compactifications Solve the Cosmological Constant Problem?

TL;DR

This paper critically examines claims that certain higher-dimensional compactifications can solve the cosmological constant problem, arguing that these models overlook the core issue of why mbda is much smaller than other physical scales.

Contribution

The paper clarifies that existing toy models do not address the true cosmological constant problem and provides a general argument about the role of moduli and Planck mass in this context.

Findings

Toy models remove or set to zero other mass scales, ignoring the real problem.

Including realistic mass scales reintroduces the problem, often requiring accidental cancellations.

Models that set moduli masses to zero trivially solve mbda, but are physically unmotivated.

Abstract

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.