Lagrangian perturbations and the matter bispectrum II: the resummed one-loop correction to the matter bispectrum

This is part two in a series of papers in which we investigate an approach based on Lagrangian perturbation theory (LPT) to study the non-linear evolution of the large-scale structure distribution in the universe. Firstly, we compute the matter bispectrum in real space using LPT up one-loop order, for both Gaussian and non-Gaussian initial conditions. In the initial position limit, we find that the one-loop bispectrum computed in this manner is identical to its counterpart obtained from standard Eulerian perturbation theory (SPT). Furthermore, the LPT formalism allows for a simple reorganisation of the perturbative series corresponding to the resummation of an infinite series of perturbations in SPT. Applying this method, we find a resummed one-loop bispectrum that compares favourably with results from N-body simulations. We generalise the resummation method also to the computation of the redshift-space bispectrum up to one loop.

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