Radiative stability of tiny cosmological constant from the Swampland and quantized compactification

TL;DR

This paper proposes a quantization mechanism for the cosmological constant based on circle compactification and Swampland constraints, suggesting that the allowed values of the cosmological constant are discrete and potentially stable against quantum corrections.

Contribution

It introduces a novel quantization rule for the cosmological constant linked to the compactification radius, providing a new perspective on its small observed value.

Findings

The compactification radius and cosmological constant are quantized.

Allowed cosmological constant values follow a $ abla o n^2$ pattern.

Quantum corrections may break the quantization, preventing large fluctuations.

Abstract

We address a quantization mechanism that can allow us to understand why the cosmological constant is not large under the quantum corrections from studying the circle compactification solution of the Standard Model coupled to Einstein gravity which is subject to the constraint of the Swampland conjectures. A novel result in the present work compared to the previous investigations in the literature is that the radius of the compactified dimension and the 4D cosmological constant $\Lambda_4$ must in fact be quantized. The quantization rule of the cosmological constant is given by $\Lambda_4\propto n^2$ with $n=1,2,3,4,\ldots$, which means that the values of $\Lambda_4$ are not arbitrary but only its specific values are allowed. In general, the quantum corrections as well as other effects would break this quantization rule. Hence, it could prevent the quantum fluctuations from generating zero-point energy contributions to the cosmological constant.