Propagators in Lagrangian space

TL;DR

This paper investigates the behavior of propagators in Lagrangian space, revealing they do not decay exponentially like in Eulerian space and instead track linear growth with a renormalized amplitude, offering new insights into cosmic structure evolution.

Contribution

It introduces a novel method for analyzing Lagrangian propagators, showing they differ fundamentally from Eulerian propagators and highlighting the role of vorticity in these differences.

Findings

Lagrangian propagators are non-monotonic over time.

They track the linear growth rate at late times with renormalized amplitude.

Differences are linked to vorticity degrees of freedom.

Abstract

It has been found recently that propagators, e.g. the cross-correlation spectra of the cosmic fields with the initial density field, decay exponentially at large-k in an Eulerian description of the dynamics. We explore here similar quantities defined for a Lagrangian space description. We find that propagators in Lagrangian space do not exhibit the same properties: they are found not to be monotonic functions of time, and to track back the linear growth rate at late time (but with a renormalized amplitude). These results have been obtained with a novel method which we describe alongside. It allows the formal resummation of the same set of diagrams as those that led to the known results in Eulerian space. We provide a tentative explanation for the marked differences seen between the Eulerian and the Lagrangian cases, and we point out the role played by the vorticity degrees of freedom that are specific to the Lagrangian formalism. This provides us with new insights into the late-time behavior of the propagators.