Lagrangian perturbation theory at one loop order: successes, failures, and improvements

Abstract

We apply the convolved Lagrangian perturbation theory (CLPT) formalism, in which one can express the matter density power spectrum in terms of integrals over a function of cumulants of the displacement field, allowing for a resummation of the terms, to evaluate the full one loop power spectrum. We keep the cumulants up to third order, extending the Zel'dovich approximation and providing the power spectrum analogous to the calculations recently performed for the correlation function. We compare the results to the N-body simulations and to the Lagrangian perturbation simulations up to the second order. We find that the analytic calculations are in a good agreement with the LPT simulations, but when compared to full N-body simulations, we find that while one loop calculations improve upon the Zel'dovich approximation in the power spectrum, they still significantly lack power. As found previously in the correlation function one loop CLPT improves slightly against Zel'dovich above 30Mpc/h, but is actually worse than Zel'dovich below that. We investigate the deficiencies of the CLPT approach and argue that main problem of CLPT is its inability to trap particles inside dark matter halos, which leads to an overestimate of the small scale power of the displacement field and to an underestimate of the small scale power from one halo term effects. We model this using the displacement field damped at a nonlinear scale (CLPTs). To explore this in more detail we decompose the power spectrum and correlation function into three additive components: Zel'dovich, residual BAO wiggle, and residual broad band. One loop CLPT predicts small modifications to BAO wiggles that are enhanced in CLPTs, with up to 5\% corrections to correlation function around BAO scale.

19 pages, 8 figures

References in corpus (11)

• Transients from Initial Conditions in Cosmological Simulations
• The Effective Field Theory of Cosmological Large Scale Structures
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• A critical look at cosmological perturbation theory techniques
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Multi-Point Propagators in Cosmological Gravitational Instability
• A Closure Theory for Non-linear Evolution of Cosmological Power Spectra
• Dark matter clustering: a simple renormalization group approach
• Analytic model for the matter power spectrum, its covariance matrix, and baryonic effects
• Large-N expansions applied to gravitational clustering
• Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering

Cited by in corpus (25)

• Redshift-Space Distortions in Lagrangian Perturbation Theory
• Consistent Modeling of Velocity Statistics and Redshift-Space Distortions in One-Loop Perturbation Theory
• The Gaussian streaming model and Lagrangian effective field theory
• Reconstruction within the Zeldovich approximation
• Testing Screened Modified Gravity
• Modeling CMB Lensing Cross Correlations with {\sc CLEFT}
• Halo Zeldovich model and perturbation theory: dark matter power spectrum and correlation function
• FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals
• How smooth are particle trajectories in a $\Lambda$CDM Universe?
• Large-scale structure perturbation theory without losing stream crossing
• Accurate predictions from small boxes: variance suppression via the Zel'dovich approximation
• Precision Redshift-Space Galaxy Power Spectra using Zel'dovich Control Variates
• Convolution Lagrangian perturbation theory for biased tracers beyond general relativity
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• Marked correlation functions in perturbation theory
• Perturbation theory of LSS in the $\Lambda$CDM Universe: exact time evolution and the two-loop power spectrum
• Galaxy clustering from the bottom up: A Streaming Model emulator I
• Lensing smoothing of BAO wiggles
• Analytical growth functions for cosmic structures in a $\Lambda$CDM Universe
• BullFrog: Multi-step perturbation theory as a time integrator for cosmological simulations
• Projection of the gravitational dynamics on a subspace of probability distributions: curl-free Gaussian ansatz
• Lagrangian-space Gaussian ansatz for the matter redshift-space power spectrum and correlation function
• Lagrangian Perturbation Theory for Biased Tracers: Significance of the Number Conservation
• Improving cosmological covariance matrices with machine learning
• Gravitational redshift from large-scale structure: nonlinearities, antisymmetries, and the dipole