A Closure Theory for Nonlinear Evolution of Cosmological Power Spectra

Taruya, Atsushi; Hiramatsu, Takashi

doi:10.1086/526515

Cited by 160 publications

(270 citation statements)

References 38 publications

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“…2008; Taruya & Hiramatsu 2008;Carlson et al 2009), the 1-loop standard perturbation theory overestimates the power on these scales, especially at low redshift. The dashed curves shown in Fig.…”

Section: Eulerian Perturbation Theoriesmentioning

confidence: 95%

“…However, this regime should be within the range of validity of perturbation theories, which offer the advantage of systematic and reliable predictions, without fitting parameters. This has led to a renewed interest in perturbative approaches in recent years, as it may be possible to improve over the standard perturbation theory (Goroff et al 1986;Bernardeau et al 2002) by using resummation schemes that allow partial resummations of higher order terms (Crocce & Scoccimarro 2006b,a;Valageas 2007a;Matarrese & Pietroni 2007;Taruya & Hiramatsu 2008;Valageas 2008;Pietroni 2008;Matsubara 2008). In particular, this somewhat improves the accuracy of the predicted matter power spectrum on the large scales associated with BAO, as compared with standard perturbation theory truncated at the same order (Crocce & Scoccimarro 2008;Carlson et al 2009;Taruya et al 2009).…”

Section: Introductionmentioning

confidence: 99%

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Combining perturbation theories with halo models

Valageas

Nishimichi

2011

A&A

142

216

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Aims. We investigate the building of unified models that can predict the matter-density power spectrum and the two-point correlation function from very large to small scales, being consistent with perturbation theory at low k and with halo models at high k. Methods. We use a Lagrangian framework to re-interpret the halo model and to decompose the power spectrum into "2-halo" and "1-halo" contributions, related to "perturbative" and "non-perturbative" terms. We describe a simple implementation of this model and present a detailed comparison with numerical simulations, from k ∼ 0.02 up to 100 h Mpc −1 , and from x ∼ 0.02 up to 150 h −1 Mpc. Results. We show that the 1-halo contribution contains a counterterm that ensures a k 2 tail at low k and this contribution is important not to spoil the predictions on the scales probed by baryon acoustic oscillations, k ∼ 0.02 to 0.3 h Mpc −1 . On the other hand, we show that standard perturbation theory is inadequate for the 2-halo contribution, because higher order terms grow too fast at high k, so that resummation schemes must be used. Moreover, we explain why such a model, which is based on the combination of perturbation theories and halo models, remains consistent with standard perturbation theory up to the order of the resummation scheme. We describe a simple implementation, based on a 1-loop "direct steepest-descent" resummation for the 2-halo contribution that allows fast numerical computations, and we check that we obtain a good match to simulations at low and high k. We also study the dependence of such predictions on the details of the underlying model, such as the choice of the perturbative resummation scheme or the properties of halo profiles. Our simple implementation already fares better than both standard 1-loop perturbation theory on large scales and simple fits to the power spectrum at high k, with a typical accuracy of 1% on large scales and 10% on small scales. We obtain similar results for the two-point correlation function. However, there remains room for improvement on the transition scale between the 2-halo and 1-halo contributions, which may be the most difficult regime to describe.

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Section: Eulerian Perturbation Theoriesmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Combining perturbation theories with halo models

Valageas

Nishimichi

2011

A&A

142

216

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show abstract

“…This has led to tremendous progress in structure formation theory in the last several decades. In particular, nonlinear perturbation theory (PT), both Eulerian and Lagrangian (Bernardeau et al 2002), has evolved into sophisticated forms (Crocce & Scoccimarro 2006a, 2006bBernardeau et al 2008;Matsubara 2008;Pietroni 2008;Taruya & Hiramatsu 2008) that could provide a very accurate estimation of the matter clustering in the weakly nonlinear regime. In the deeply nonlinear region, however, PT performs poorly.…”

Section: Introductionmentioning

confidence: 99%

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

Wang

Szalay

2016

ApJ

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The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel'dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

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“…On the other hand, Valageas (2007a) describes a path-integral formalism that allows applying the tools of field theory, such as large-N expansions, to compute the power spectrum and higher order statistics like the bispectrum (Valageas 2008). One of these large-N expansions was recovered by Taruya & Hiramatsu (2008), as a "closure theory" where one closes the hierarchy of equations satisfied by the many body correlations at the third order, following the "direct interaction approximation" introduced in hydrodynamics (Kraichnan 1959). This also improves the predictions for the power spectrum on the scales probed by the baryonic acoustic oscillations (Taruya et al 2009;Valageas & Nishimichi 2010).…”

Section: Introductionmentioning

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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A Closure Theory for Nonlinear Evolution of Cosmological Power Spectra

Cited by 160 publications

References 38 publications

Combining perturbation theories with halo models

Combining perturbation theories with halo models

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

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

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