Testing approximations for non-linear gravitational clustering

Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

doi:10.1093/mnras/260.4.765

Cited by 166 publications

(232 citation statements)

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“…Since the Zeldovich dynamics provides a reasonable approximation of the gravitational dynamics down to weakly nonlinear scales (Coles et al 1993;Pauls & Melott 1995), and its accuracy can be improved by implementing the "adhesion model" that only differs after shell crossing (Weinberg & Gunn 1990;Melott et al 1994;Sathyaprakash et al 1995), we can expect that to a large extent these results still apply to the gravitational case. In particular, while we find that at z = 0 the nonperturbative correction to the density power spectrum is around 1% at k ∼ 0.23 h Mpc −1 and 50% at k ∼ 0.9 h Mpc −1 , Afshordi (2007) finds the wavenumbers k ∼ 0.1 h Mpc −1 and k ∼ 0.85 h Mpc −1 with a phenomenological "sticky halo model".…”

Section: Perturbative and Nonperturbative Contributionsmentioning

confidence: 99%

Impact of shell crossing and scope of perturbative approaches, in real and redshift space

Valageas¹

2010

A&A

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Aims. We study the effect of nonperturbative corrections associated with the behavior of particles after shell crossing on the matter power spectrum. We compare their amplitude with the perturbative terms that can be obtained within the fluid description of the system, to estimate the range of scales where such perturbative approaches are relevant. Methods. We use the simple Zeldovich dynamics as a benchmark, as it allows the exact computation of the full nonlinear power spectrum and of perturbative terms at all orders. Then, we introduce a "sticky model" that coincides with the Zeldovich dynamics before shell crossing but shows a different behavior afterwards. Thus, their power spectra only differ in their nonperturbative terms. We consider both the real-space and redshift-space power spectra. Results. We find that the potential of perturbative schemes is greater at higher redshift for a ΛCDM cosmology. For the real-space power spectrum, one can go up to order 66 of perturbation theory at z = 3, and to order 9 at z = 0, before the nonperturbative correction surpasses the perturbative correction of that order. This allows us to increase the upper bound on k where systematic theoretical predictions may be obtained by perturbative schemes, beyond the linear regime, by a factor ∼26 at z = 3 and ∼6.5 at z = 0. This provides a strong motivation to study perturbative resummation schemes, especially at high redshifts z ≥ 1. In the context of cosmological reconstruction methods, the Monge-Ampère-Kantorovich scheme appears to be close to optimal at z = 0. There also seems to be little room for improvement over current reconstruction methods of the baryon acoustic oscillations at z = 0. This can be understood from the small number of perturbative terms that are relevant at z = 0, before nonperturbative corrections dominate. We also point out that the rise of the power spectrum on the transition scale to the nonlinear regime strongly depends on the behavior of the system after shell crossing. We find similar results for the redshift-space power spectrum, with characteristic wavenumbers that are shifted to lower values as redshift-space distortions amplify higher order terms of the perturbative expansions while decreasing the resummed nonlinear power at high k.

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Section: Perturbative and Nonperturbative Contributionsmentioning

confidence: 99%

Impact of shell crossing and scope of perturbative approaches, in real and redshift space

Valageas¹

2010

A&A

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“…The unexpected result may be caused by construction of the first-order approximation, in which the strength of the pressure effect is determined only by the coefficient (1/a 2 ) dP/dρ(ρ b ) in the fourth term of the left side of Eq. (20). The square of the 'sound speed,' dP/dρ, which is contained in the coefficient, is originally a function of ρ, but now in the coefficient ρ is replaced with ρ b…”

Section: First-order Solutionsmentioning

confidence: 99%

“…In these figures, the difference between the first-and second-order approximations seems still small on large scales (compare (a) and (b), and (c) and (d)), although the secondorder solutions should compensate shortcomings of the first-order approximation on small scales, as was discussed by Buchert and Ehlers [19] for the dust case. [20,21,22], which yields a coarse-grained density field of the original Zel'dovich approximation.…”

Section: B Density Field In a Two-dimensional Modelmentioning

confidence: 99%

Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion

Tatekawa¹,

Suda²,

Maeda³

et al. 2002

Phys. Rev. D

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We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method up to second order. This perturbative approach is an extension of the usual Lagrangian perturbation theory for a pressureless fluid, in view of inclusion of the pressure effect, which should be taken into account on the occurrence of velocity dispersion. We obtain the first-order solutions in generic background universes and the second-order solutions in wider range of a polytropic index, whereas our previous work gives the first-order solutions only in the Einstein-de Sitter background and the second-order solutions for the polytropic index 4/3. Using the perturbation solutions, we present illustrative examples of our formulation in one-and two-dimensional systems, and discuss how the evolution of inhomogeneities changes for the variation of the polytropic index.

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“…The former is quantified by the usual power spectrum P (k) which is however insensitive to the spatial positions of features in the realization. The latter is quantified by a cross-correlation (Coles et al 1993)…”

Section: Simulations Of Large Scale Motionsmentioning

confidence: 99%

On the accuracy of N-body simulations at very large scales

Rigopoulos

Valkenburg

2014

Monthly Notices of the Royal Astronomical Society

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We examine the deviation of Cold Dark Matter particle trajectories from the Newtonian result as the size of the region under study becomes comparable to or exceeds the particle horizon. To first order in the gravitational potential, the general relativistic result coincides with the Zel'dovich approximation and hence the Newtonian prediction on all scales. At second order, General Relativity predicts corrections which overtake the corresponding second order Newtonian terms above a certain scale of the order of the Hubble radius. However, since second order corrections are very much suppressed on such scales, we conclude that simulations which exceed the particle horizon but use Newtonian equations to evolve the particles, reproduce the correct trajectories very well. The dominant relativistic corrections to the power spectrum on scales close to the horizon are at most of the order of ∼ 10 −5 at z = 49 and ∼ 10 −3 at z = 0. The differences in the positions of real space features are affected at a level below 10 −6 at both redshifts. Our analysis also clarifies the relation of N-body results to relativistic considerations.

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Testing approximations for non-linear gravitational clustering

Cited by 166 publications

References 0 publications

Impact of shell crossing and scope of perturbative approaches, in real and redshift space

Impact of shell crossing and scope of perturbative approaches, in real and redshift space

Perturbation theory in Lagrangian hydrodynamics for a cosmological fluid with velocity dispersion

On the accuracy of N-body simulations at very large scales

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