Critical look at cosmological perturbation theory techniques

By Jordan Carlson, M. White, Nikhil Padmanabhan. 2009

217 citations recorded by the source corpus.

Recently, a number of analytic prescriptions for computing the nonlinear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus they must be compared with numerical simulations to assess their range of validity. We present a direct side-by-side comparison of several of these analytic approaches, using a suite of high-resolution N-body simulations as a reference, and discuss some general trends. All of the analytic results correctly predict the behavior of the power spectrum at the onset of nonlinearity, and improve upon a pure linear theory description at very large scales. All of these theories fail at sufficiently small scales. At low redshift the dynamic range in scale where perturbation theory is both relevant and reliable can be quite small. We also compute for the first time the two-loop contribution to standard perturbation theory for cold dark matter models, finding improved agreement with simulations at large redshift. At low redshifts however the two-loop term is larger than the one-loop term on quasilinear scales, indicating a breakdown of the perturbation expansion. Finally, we comment on possible implications of our results for future studies. A software package implementing themore » methods presented here is available at http://mwhite.berkeley.edu/Copter.« less

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/52192e77c3af95463862b528817a1963dee87023

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Citations in the corpus

THE COYOTE UNIVERSE. III. SIMULATION SUITE AND PRECISION EMULATOR FOR THE NONLINEAR MATTER POWER SPECTRUM (2009, background): “A similar result can also be found in Carlson et al. (2009).”
The Effective Field Theory of Large Scale Structures at two loops (2013, methodology): “ veried that indeed the EFTofLSS is able to make predictions for the scaling universes. From the perspective of the EFTofLSS, the previous approaches like SPT and relatives (see for example [3,4] or [5]) are missing important terms in the equations of motion. Once these terms are included, perturbat”
Nonlinear perturbation theory extension of the Boltzmann code CLASS (2020, methodology): “To the best of our knowledge, this begins with COPTER [18], which was designed to compute the 1-loop and 2-loop matter power spectra in Standard Perturbation Theory (SPT) and its extensions.”
Cosmological non-linearities as an effective fluid (2010, background): “[20] recently demonstrated, on small scales one-loop perturbation theory becomes increasingly unreliable in capturing even the correct qualitative features of the velocity-density cross-correlation.”
THE COYOTE UNIVERSE. II. COSMOLOGICAL MODELS AND PRECISION EMULATION OF THE NONLINEAR MATTER POWER SPECTRUM (2009, background): “…might offer an alternative path to obtaining precise predictions for the nonlinear matter power spectrum (see, e.g., Crocce & Scoccimarro 2006; Matsubara 2008; Pietroni 2008; Carlson et al. 2009; Padmanabhan & White 2009; and references therein), and provide a useful foil for the numerical results.”
The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9 (2011, methodology): “Standard perturbation theory at z = 0 is only accurate for the range k < 0.1 h Mpc−1, but other expansion approaches are available with the precise range of validity dependent on the model in question and the accuracy required (Nishimichi et al. 2009, Carlson et al. 2009).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Testing gravity with redshift-space distortions using the power spectrum multipoles (2013, methodology): “…we want to make use of the power spectrum beyond k = 0.10 h Mpc−1 we cannot rely on standard PT which seems to break down at low redshift for k > 0.10 h Mpc−1, where the 2-loop term turns out to be larger than the 1-loop term (Crocce & Scoccimarro 2006; Carlson et al. 2009; Taruya et al. 2009).”
Observational probes of cosmic acceleration (2012, methodology): “However, the shape of the power spectrum does change on scales approaching knl, in ways that can be calculated using N-body simulations (Heitmann et al., 2010) or several variants of cosmological perturbation theory (Carlson et al. 2009 and references therein).”
The effective field theory of cosmological large scale structures (2012, background): “An incomplete sample of these works is given by [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25].”
THE COYOTE UNIVERSE. I. PRECISION DETERMINATION OF THE NONLINEAR MATTER POWER SPECTRUM (2008, background): “Perturbation theory has errors on the mass power spectrum currently estimated to be at the percent level in the weakly nonlinear regime (see, e.g., Jeong & Komatsu 2006; Carlson et al. 2009 for recent treatments or Bernardeau et al. 2002 for an earlier review).”
Matter power spectrum and the challenge of percent accuracy (2015, background): “Standard perturbation theory gives accurate results up to k ∼ 0.1 hMpc−1, while numerical simulations are indispensable at higher wave numbers (Carlson et al. 2009; Fosalba et al. 2015).”