What sets the very small value of the cosmological constant — the energy density that drives the Universe’s accelerated expansion — is a long‑standing puzzle. This paper argues that the answer may lie in the enormous entropy associated with the de Sitter horizon, the thermal surface that surrounds a spacetime with positive cosmological constant. The authors identify a single dimensionless number, called α, fixed by the ratio of the de Sitter length scale to the Planck length, and show that α admits a natural interpretation as the Bekenstein–Hawking entropy of the de Sitter horizon.

The researchers start from a version of gravity that is symmetric under local rescaling of lengths, a symmetry called Weyl or conformal symmetry. When that symmetry is broken, the usual Einstein description of gravity with a cosmological constant emerges and leaves behind a residual global scale symmetry. In this residual description the action of gravity can be written in terms of the single dimensionless coupling α, which the authors relate to the horizon entropy and therefore to the microscopic number of degrees of freedom that live on or are associated with the de Sitter horizon.

To give α a microscopic meaning they combine several modern ideas: emergent gravity (the idea that spacetime and gravity are coarse‑grained, collective phenomena), holography (relations between a gravitational bulk and a lower‑dimensional non‑gravitational theory), and the functional renormalization group (FRG), a tool for tracking how physical quantities change with scale. In this picture α becomes scale dependent, α(k), and its renormalization‑group flow encodes how the effective number of horizon degrees of freedom changes when one probes the system at different length scales.

A key assumption the authors make is that α(k) increases monotonically toward the infrared (toward larger scales). This monotonicity is motivated by the entropic interpretation of α and by analogies with theorems in conformal field theory that constrain how central charges change with scale. Under that requirement, and within the FRG approach and the approximations they use, the infrared value of the cosmological constant comes out to be of the same order as the observed one. In plain terms, the cosmological constant’s tiny value is then linked to the extremely large number of microscopic horizon degrees of freedom in our de Sitter‑like universe.