On the reach of perturbative descriptions for dark matter displacement fields

Understand

We study Lagrangian Perturbation Theory (LPT) and its regularization in the Effective Field Theory (EFT) approach.

• We evaluate the LPT displacement with the same phases as a corresponding $N$-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra.
• We reliably detect a non-vanishing leading order EFT coefficient and a stochastic displacement term, uncorrelated with the LPT terms.
• This stochastic term is expected in the EFT framework, and, to the best of our understanding, is not an artifact of numerical errors or transients in our simulations.