Standard cosmological perturbation theory (SPT) for the Large Scale Structure (LSS) of the Universe fails at small scales (UV) due to strong nonlinearities and to multistreaming effects. In Pietroni et al. 2011 a new framework was proposed in which t
he large scales (IR) are treated perturbatively while the information on the UV, mainly small scale velocity dispersion, is obtained by nonlinear methods like N-body simulations. Here we develop this approach, showing that it is possible to reproduce the fully nonlinear power spectrum (PS) by combining a simple (and fast) 1-loop computation for the IR scales and the measurement of a single, dominant, correlator from N-body simulations for the UV ones. We measure this correlator for a suite of seven different cosmologies, and we show that its inclusion in our perturbation scheme reproduces the fully non-linear PS with percent level accuracy, for wave numbers up to $ksim 0.4, h~{rm Mpc^{-1}}$ down to $z=0$. We then show that, once this correlator has been measured in a given cosmology, there is no need to run a new simulation for a different cosmology in the suite. Indeed, by rescaling this correlator by a proper function computable in SPT, the reconstruction procedure works also for the other cosmologies and for all redshifts, with comparable accuracy. Finally, we clarify the relation of this approach to the Effective Field Theory methods recently proposed in the LSS context.
We quantify the impact of massive neutrinos on the statistics of low density regions in the intergalactic medium (IGM) as probed by the Lyman-alpha forest at redshifts z=2.2--4. Based on mock but realistic quasar (QSO) spectra extracted from hydrodyn
amic simulations with cold dark matter, baryons and neutrinos, we find that the probability distribution of weak Lyman-alpha absorption features, as sampled by Lyman-alpha flux regions at high transmissivity, is strongly affected by the presence of massive neutrinos. We show that systematic errors affecting the Lyman-alpha forest reduce but do not erase the neutrino signal. Using the Fisher matrix formalism, we conclude that the sum of the neutrino masses can be measured, using the method proposed in this paper, with a precision smaller than 0.4 eV using a catalog of 200 high resolution (S/N~100) QSO spectra. This number reduces to 0.27 eV by making use of reasonable priors in the other parameters that also affect the statistics of the high transitivity regions of the Lyman-alpha forest. The constraints obtained with this method can be combined with independent bounds from the CMB, large scale structures and measurements of the matter power spectrum from the Lyman-alpha forest to produce tighter upper limits on the sum of the masses of the neutrinos.
