Using Lagrangian perturbation theory for precision cosmology

Abstract

We explore the Lagrangian perturbation theory (LPT) at 1-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum in LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in the Lagrangian perturbation theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the 1-loop solution in LPT to the 2-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the 2-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at $k=0.2$ $h{\mathrm{Mpc}}^{-1}$ and $z=0.35$ to better than 2%.

35 pages, 9 figures

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• Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations
• Lagrangian perturbation theory for modified gravity
• Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues
• Understanding redshift space distortions in density-weighted peculiar velocity
• A direct measure of free electron gas via the Kinematic Sunyaev-Zel'dovich effect in Fourier-space analysis
• Renormalization of Lagrangian bias via spectral parameters
• Statistics of biased tracers in variance-suppressed simulations
• Modeling iterative reconstruction and displacement field in the large scale structure
• Approximate methods for the generation of dark matter halo catalogs in the age of precision cosmology
• Cosmological perturbation theory for large scale structure in phase space