Does the cosmological constant stay hidden?

TL;DR

This paper investigates whether the cosmological constant can be concealed within complex Planck-scale topologies, analyzing the stability of solutions where the average expansion remains zero despite a large cosmological constant.

Contribution

It develops a differential equation for the evolution of the average expansion scalar and examines the stability of solutions where the cosmological constant is effectively hidden.

Findings

The solution with zero average expansion appears unstable.

Hiding the cosmological constant in complex topology may not be stable.

The analysis suggests limitations to the hiding mechanism for the cosmological constant.

Abstract

We elaborate on the proposal of [Phys. Rev. Lett. 123 (2019) 13, 131302], about the possibility of hiding the cosmological constant in the complicated topology that one expects to exist at the Planck scale. We build a differential equation ruling the time evolution of $\langle K\rangle$, the spatial average of the expansion scalar. Supposing that the solution $\langle K\rangle = 0$ exists despite the presence of a large cosmological constant $\Lambda$, we show that such solution seems to be unstable.