Symmetries and Consistency Relations in the Large Scale Structure of the Universe

TL;DR

The paper identifies and analyzes the symmetry structure of the Newtonian fluid equations describing gravitational instability in the universe, revealing Galilean, acceleration, and Lifshitz-type invariances that shape the nonlinear evolution of structure. It connects these 4D cosmological symmetries to a higher-dimensional Bargmann/Schrödinger framework via dimensional reduction, clarifying the geometric origin of the invariances and their behavior under cosmic expansion. By deriving Ward identities and a universal squeezed-limit consistency relation for (n+1)-point correlators, the work provides powerful, model-independent consistency checks for perturbation theories and gravity models used in large-scale-structure analyses. The results offer practical tests for galaxy surveys and potential signals of modified gravity through symmetry breaking, with explicit expressions for the soft-limit correlators.)

Abstract

We study the symmetries enjoyed by the Newtonian equations of motion of the non-relativistic dark matter fluid coupled to gravity which give rise to the phenomenon of gravitational instability. We also discuss some consistency relations involving the soft limit of the (n + 1)-correlator functions of matter and galaxy overdensities.