Symmetries of cosmological perturbations: The residual low multipole ambiguity

TL;DR

This work recasts long-wavelength cosmological perturbations as large gauge transformations (LGTs) in the Newtonian gauge and shows two key advances: (i) LGTs extend to local, infinite-dimensional soft symmetries with time-dependent generators, producing new low-multipole soft modes that physically affect the cosmological patch boundary through quasi-local quantities and reveal a cosmological frame ambiguity, and (ii) adiabatic LWMs preserve both explicit and hidden symmetries of the background, making these perturbations algebraically special (Petrov type $O$) and enabling analytic treatment via conformal and Killing structures. The authors develop the mean-curvature framework to quantify boundary observables, demonstrating that soft monopole and dipole deformations shift the patch energy and horizon, while the axial dipole induces a nonzero angular momentum. They further show that the background Killing and hidden Killing-Yano symmetries survive the dressing by LWMs, with Lie dragging mapping CKVs, KYs, and KTs from the FLRW seed to the perturbed geometries, preserving the underlying algebraic structure to first order. Altogether, the results provide a covariant, analytic handle on how large-scale perturbations influence cosmological observables and boundary charges, offering a basis for refined treatments of frame choices in cosmology and potential applications to lensing, propagation of light and gravitational waves, and the separate-universe approach.

Abstract

In cosmology, long-wavelength modes are related to large-gauge transformations (LGT), i.e. changes of coordinates that modify the physical geometry of the cosmological patch. These LGTs stand as bona-fide symmetries of cosmological perturbation theory with various applications, from consistency relations constraining cosmological correlators to non-linear conservation laws in the separate-universe approach. In this work, we revisit LGTs and derive two new results. First, we show that the global symmetries already identified in the literature can be extended to local infinite-dimensional symmetries. The associated generators depend on arbitrary functions of time, and generate low-multipole modes that modify the mean curvature energy and the angular momentum of the patch, demonstrating their physical nature. We propose to interpret these low-multipole soft modes as a new cosmological-frame ambiguity that needs to be fixed prior to evaluating cosmological observables. Second, we demonstrate that the adiabatic cosmological perturbations generated by LGTs deform but preserve all the explicit and hidden Killing symmetries of the background geometry. As such, long-wavelength modes stand as a concrete example of algebraically-special cosmological perturbations of Petrov-type O, and inherit the conformal group as isometries and a set of four deformed Killing-Yano tensors and their associated Killing tensors. This opens the possibility to study their effect on cosmological observables in a fully analytic manner.