Catelan, Lucchin, and Matarrese Reply

Catelan, Paolo; Lucchin, F.; Matarrese, S.

doi:10.1103/physrevlett.61.2627

Cited by 136 publications

(237 citation statements)

References 7 publications

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“…In general the PT expansion is more complicated because the solutions at each order become non-separable functions of τ and k [91,93,46,118]. In particular the growing mode at order n does not scale as D n 1 (τ ) (or a n (τ ) as in Eq.…”

Section: Cosmology Dependence Of Non-linear Growth Factorsmentioning

confidence: 99%

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Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver.

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Section: Cosmology Dependence Of Non-linear Growth Factorsmentioning

confidence: 99%

“…The detailed calculations can be found in [46]. Different approaches have been used in the literature to do such calculations [105,118,93]. The direct calculation appears to be the most secure, if not the rapid or most instructive.…”

Section: The Density and Velocity Fields Up To Third Ordermentioning

confidence: 99%

Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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“…The Einstein-de Sitter assumption is needed to avoid more complicated time dependence of P 13 and P 22 , but the real Universe is of course not Einstein-de Sitter. Fortunately, this is not a significant problem because, to percent level accuracy [28,60,61,62,63,64,65,66], the effect of changing the background model can be included by simply using the correct linear growth factor in Eq. (8).…”

Section: B Standard Eulerian Perturbation Theorymentioning

confidence: 99%

Dark matter clustering: A simple renormalization group approach

McDonald

2007

Phys. Rev. D

112

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I compute a renormalization group (RG) improvement to the standard beyond-linear-order Eulerian perturbation theory (PT) calculation of the power spectrum of large-scale density fluctuations in the Universe. At z = 0, for a power spectrum matching current observations, lowest order RGPT appears to be as accurate as one can test using existing numerical simulation-calibrated fitting formulas out to at least k ≃ 0.3 h Mpc −1 ; although inaccuracy is guaranteed at some level by approximations in the calculation (which can be improved in the future). In contrast, standard PT breaks down virtually as soon as beyond-linear corrections become non-negligible, on scales even larger than k = 0.1 h Mpc −1 . This extension in range of validity could substantially enhance the usefulness of PT for interpreting baryonic acoustic oscillation surveys aimed at probing dark energy, for example. I show that the predicted power spectrum converges at high k to a power law with index given by the fixed-point solution of the RG equation. I discuss many possible future directions for this line of work. The basic calculation of this paper should be easily understandable without any prior knowledge of RG methods, while a rich background of mathematical physics literature exists for the interested reader.PACS numbers: 98.65. Dx, 05.10.Cc, 95.35.+d, 98.80.Es

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“…However, the complicated non-Gaussian character of the F process can considerably complicate the calculations with respect to the linear theory case. In particular, an analytical approach based on the peaks of the F process (such as the confluent formalism of Manrique & Salvador-Solé (1995)) is essentially hopeless: an analytical description of the peaks of a random field can be obtained only for Gaussian or closely related fields (see Adler 1981), or for asymptotically high peaks (Catelan, Lucchin & Matarrese 1988). On the other hand, the simpler excursion set approach requires knowledge of only the 1-point PDF of the F process, which has been obtained above.…”

Section: Discussionmentioning

confidence: 99%

On the Cosmological Mass Function

Monaco

1997

Generation of Cosmological Large-Scale Structure

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This thesis aims to review the cosmological mass function problem, both from the theoretical and the observational point of view, and to present a new mass function theory, based on realistic approximations for the dynamics of gravitational collapse. Chapter 1 gives a general introduction on gravitational dynamics in cosmological models. Chapter 2 gives a complete review of the mass function theory. Chapters 3 and 4 present the "dynamical" mass function theory, based on truncated Lagrangian dynamics and on the excursion set approach. Chapter 5 reviews the observational state-of-the-art and the main applications of the mass function theories described before. Finally, Chapter 6 gives conclusions and future prospects.

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Catelan, Lucchin, and Matarrese Reply

Cited by 136 publications

References 7 publications

Large-scale structure of the Universe and cosmological perturbation theory

Large-scale structure of the Universe and cosmological perturbation theory

Dark matter clustering: A simple renormalization group approach

On the Cosmological Mass Function

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