Abstract. A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to k 1 h/Mpc at z > ∼ 0.5, thereby opening the possibility of applying this tool to scales interesting for weak lensing. We clarify the approximations inherent to this approach as well as its relations to previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts.

We propose a new way of looking at the Baryon Acoustic Oscillations in the Large Scale Structure clustering correlation function. We identify a scale s LP that has two fundamental features: its position is insensitive to non-linear gravity, redshift space distortions, and scale-dependent bias at the 0.5% level; it is geometrical, i.e. independent of the power spectrum of the primordial density fluctuation parameters. These two properties together make s LP , called the "linear point", an excellent cosmological standard ruler. The linear point is also appealing because it is easily identified irrespectively of how non-linearities distort the correlation function. Finally, the correlation function amplitude at s LP is similarly insensitive to non-linear corrections to within a few percent. Hence, exploiting the particular Baryon features in the correlation function, we propose three new estimators for growth measurements. A preliminary analysis of s LP in current data is encouraging.

We present the latest version of pinocchio, a code that generates catalogues of DM haloes in an approximate but fast way with respect to an N-body simulation. This code version extends the computation of particle and halo displacements up to 3rd-order Lagrangian Perturbation Theory (LPT), in contrast with previous versions that used Zeldovich approximation (ZA).We run pinocchio on the same initial configuration of a reference N-body simulation, so that the comparison extends to the object-by-object level. We consider haloes at redshifts 0 and 1, using different LPT orders either for halo construction -where displacements are needed to decide particle accretion onto a halo or halo merging -or to compute halo final positions.We compare the clustering properties of pinocchio haloes with those from the simulation by computing the power spectrum and 2-point correlation function (2PCF) in real and redshift space (monopole and quadrupole), the bispectrum and the phase difference of halo distributions. We find that 2LPT and 3LPT give noticeable improvement. 3LPT provides the best agreement with N-body when it is used to displace haloes, while 2LPT gives better results for constructing haloes. At the highest orders, linear bias is typically recovered at a few per cent level.In Fourier space and using 3LPT for halo displacements, the halo power spectrum is recovered to within 10 per cent up to k max ∼ 0.5 h/Mpc. The results presented in this paper have interesting implications for the generation of large ensemble of mock surveys aimed at accurately compute covariance matrices for clustering statistics.

One of the nicest results in cosmological perturbation theory is the analytical resummaton of the leading corrections at large momentum, which was obtained by Crocce and Scoccimarro for the propagator in [1]. Using an exact evolution equation, we generalize this result, by showing that a class of next-toleading corrections can also be resummed at all orders in perturbation theory. The new corrections modify the propagator by a few percent in the Baryonic Acoustic Oscillation range of scales, and therefore cannot be neglected in resummation schemes aiming at an accuracy compatible with future generation galaxy surveys. Similar tools can be employed to derive improved approximations for the Power Spectrum.