Matter power spectrum from a Lagrangian-space regularization of perturbation theory

We present a new approach to computing the matter density power spectrum, from large linear scales to small, highly nonlinear scales. Instead of explicitly computing a partial series of high-order diagrams, as in perturbative resummation schemes, we embed the standard perturbation theory within a realistic nonlinear Lagrangian-space ansatz. We also point out that an ``adhesion-like'' regularization of the shell-crossing regime is more realistic than a ``Zel'dovich-like'' behavior, where particles freely escape to infinity. This provides a ``cosmic web'' power spectrum with good small-scale properties that provide a good matching with a halo model on mildly nonlinear scales. We obtain a good agreement with numerical simulations on large scales, better than 3% for k1h Mpc^-1, and on small scales, better than 10% for k10h Mpc^-1, at z0. 35, which improves over previous methods.