Quantum of the bare cosmological constant

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 $\lambda_B>0$.