Higher-spin charges and the $L_{\Lambda} w_{1 + \infty}$ algebra in (A)dS$_4$

Abstract

We consider $(3+1)$-dimensional asymptotically locally (anti-)de Sitter ((A)dS$_4$) spacetimes with boundary conditions allowing for gravitational flux. We construct an infinite tower of higher-spin charges as perturbative solutions in the cosmological constant $\Lambda$ to a hierarchy of evolution equations resulting from an asymptotic expansion of the Einstein equations. We show that these charges canonically realize the $\Lambda$-deformed $w_{1+\infty}$ algebra ($L_{\Lambda} w_{1+\infty}$) on a restricted gravitational phase space, thereby extending the higher-spin symmetry structure of asymptotically flat spacetimes to asymptotically (A)dS spacetimes. We further construct the curved-space counterparts of conformally soft gravitons directly in terms of spacetime data. We show that they are primaries with respect to an $\mathfrak{sl}(2,\mathbb{R})$ subalgebra of the (A)dS$_4$ isometry algebra and that their Poisson brackets with the quadratic higher-spin charges reproduce the $\Lambda$-deformed celestial operator product expansion proposed by Taylor and Zhu. Our results establish the bulk gravitational origin of the $L_{\Lambda}w_{1+\infty}$ symmetry and extend the celestial bulk-boundary dictionary to asymptotically (A)dS$_4$ gravity.