Estimating CDM Particle Trajectories in the Mildly Non-Linear Regime of Structure Formation. Implications for the Density Field in Real and Redshift Space

We obtain approximations for the CDM particle trajectories starting from Lagrangian Perturbation Theory. These estimates for the CDM trajectories result in approximations for the density in real and redshift space, as well as for the momentum density that are better than what standard Eulerian and Lagrangian perturbation theory give. For the real space density, we find that our proposed approximation gives a good cross-correlation (>95%) with the non-linear density down to scales almost twice smaller than the non-linear scale, and six times smaller than the corresponding scale obtained using linear theory. This allows for a speed-up of an order of magnitude or more in the scanning of the cosmological parameter space with N-body simulations for the scales relevant for the baryon acoustic oscillations. Possible future applications of our method include baryon acoustic peak reconstruction, building mock galaxy catalogs, momentum field reconstruction.Comment: 25 pages, 11 figures; reference adde

Non-linear Galaxy Power Spectrum and Cosmological Parameters

The galaxy power spectrum is now a well-known tool of precision cosmology. In addition to the overall shape, baryon oscillations and the small-scale suppression of power by massive neutrinos capture complimentary information on cosmological parameters when compared to the angular power spectrum of cosmic microwave background anisotropies. We study both the real space and redshift space galaxy power spectra in the context of non-linear effects and model them based on the halo approach to large scale structure clustering. We consider potential systematic in the cosmological parameter determination when non-linear effects are ignored and the galaxy power spectrum is described with the linear power spectrum scaled by a constant bias factor. We suggest that significant improvements can be made when non-linear effects are taken into account as a power-law contribution with two additional parameters to be determined from the data. In addition to cosmological parameters through galaxy clustering, such an approach allow a determination of useful information related to astrophysics on how galaxies occupy dark matter halos.Comment: 14 pages, 6 figures; MNRAS in pres

Scale invariant distribution functions in quantum systems with few degrees of freedom

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.Comment: 8+10 pages. Scipost Submissio

Scale invariant distribution functions in quantum systems with few degrees of freedom

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.Comment: 8+10 pages. Scipost Submissio