Cluster algebras for cosmological correlators

In this paper, we explore the cluster algebras for symbol letters or singularities of cosmological correlators in a conformally coupled scalar field theory. We show that the symbol letters for tree-level n-site ladder cosmological correlators are governed by A_{2(n-1)} cluster algebras. Additionally, we demonstrate that the symbol letters for one-loop bubble cosmological correlator are an union of two A_3 cluster algebras. The algebras relations of letters will provide an important tool to bootstrap analytic cosmological correlators.