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

We present a new approach to compute 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 provides 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 $k≤ 1 h$Mpc$^-1$, and on small scales, better than 10% for $k ≤ 10 h$Mpc$^-1$, at $z ≥ 0.35$, which improves over previous methods.