Quantum of the bare cosmological constant

TL;DR

This paper explores scalar field theories in curved spacetimes where modes are localized on lower-dimensional hypersurfaces, revealing how the bare cosmological constant influences the symmetry of classical solutions.

Contribution

It introduces localized scalar field modes in curved spacetimes and analyzes their symmetry properties related to the bare cosmological constant.

Findings

Localized modes exist on hypersurfaces of dimension d≤D.

Symmetry groups depend on the sign of the bare cosmological constant.

Distinct symmetry structures are identified for different values of λ_B.

Abstract

We show that there exist scalar field theories with plausible one-particle states in general $D$ dimensional nonstationary curved spacetimes whose propagating modes are localized on $d\le D$ dimensional hypersurfaces, and the corresponding stress tensor resembles the bare cosmological constant $\lambda_B$ in the $D$ dimensional bulk. We show that nontrivial $d=1$ dimensional solutions correspond to $\lambda_B< 0$. Considering free scalar theories we find that for $d=2$ the symmetry of the parameter space of classical solutions corresponding to $\lambda_B\neq 0$ is $O(1,1)$ which enhances to $\mathbb{Z}_2\times{\rm Diff}(\mathbb{R}^1)$ at $\lambda_B=0$. For $d>2$ we obtain $O(d-1,1)$, $O(d-1)\times {\rm Diff}(\mathbb{R}^1)$ and $O(d-1,1)\times O(d-2)\times {\rm Diff}(\mathbb{R}^1)$ corresponding to, respectively, $\lambda_B<0$, $\lambda_B=0$ and $\lambda_B>0$.