MPTbreeze: A fast renormalized perturbative scheme

We put forward and test a simple description of multipoint propagators (MP), which serve as building blocks to calculate the non-linear matter power spectrum. On large scales these propagators reduce to the well-known kernels in standard perturbation theory, while at smaller scales they are suppressed due to non-linear couplings. Through extensive testing with numerical simulations we find that this decay is characterized by the same damping scale for both two- and three-point propagators. In turn this transition can be well modelled with resummation results that exponentiate one-loop computations. For the first time, we measure the four components of the non-linear (two-point) propagator using dedicated simulations started from two independent random Gaussian fields for positions and velocities, verifying in detail the fundamentals of propagator resummation. We use these results to develop an implementation of the MP expansion for the non-linear power spectrum that only requires seconds to evaluate at baryon acoustic oscillations (BAO) scales. To test it we construct six suites of large numerical simulations with different cosmologies. From these and LasDamas runs we show that the non-linear power spectrum can be described at the ≲ 2 per cent level at BAO scales for redshifts in the range [0-2.5]. We make a public release of the MPTbreeze code with the hope that it can be useful to the community.