Non-linear Fields in Generalized Cosmologies

The perturbative approach to structure formation has recently received a lot of attention in the literature. In such setups the final predictions for observables like the power spectrum is often derived under additional approximations such as a simplified time dependence. Here we provide all-order perturbative integral solutions for density and velocity fields in generalized cosmologies, with a direct application to clustering quintessence. We go beyond the standard results based on extending the EdS-like approximations. As an illustrative example, we apply our findings to the calculation of the one-loop power spectrum of density and momentum fields. We find corrections close to $1\%$ in the mildly non-linear regime of $\Lambda$CDM cosmologies for the density power spectrum, while in the case of the density-momentum power spectrum effects can reach up to $1.5\%$ for $k\sim 0.2h/$Mpc.