Propagators in Lagrangian space

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.

14 pages, 5 figures

References in corpus (15)

• Stable clustering, the halo model and nonlinear cosmological power spectra
• Halo Models of Large Scale Structure
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Nonlinear evolution of cosmological power spectra
• Renormalized Cosmological Perturbation Theory
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• Nonlinear Evolution of Baryon Acoustic Oscillations
• Memory of Initial Conditions in Gravitational Clustering
• Resumming Cosmic Perturbations
• Dark matter clustering: a simple renormalization group approach
• The Nonlinear Evolution of Rare Events
• Large-N expansions applied to gravitational clustering
• A new approach to gravitational clustering: a path-integral formalism and large-N expansions
• Using the Zeldovich dynamics to test expansion schemes
• Vorticity generation in large-scale structure caustics

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