Renormalized cosmological perturbation theory

Crocce, M.; Scoccimarro, Román

doi:10.1103/physrevd.73.063519

Cited by 570 publications

(1,311 citation statements)

References 35 publications

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“…In some cases, it may be sufficient to resum the contributions of IR modes from all loop orders. Such dynamics should be well described by the perfect fluid equations, and several techniques have been developed to do this (see for example [4,15,16,17] 8 )…”

Section: Dimensional Analysis For the Real Universementioning

confidence: 99%

“…not a so-called IR-safe quantity). For this reason, it might well be that results will improve after the IR modes have been properly resummed, along the lines of the techniques derived in [4,15,16,17]. We leave this as well to future work.…”

Section: Predictions For Correlation Functions Involving Momentummentioning

confidence: 99%

“…Since we are interested in computing correlation functions for δ(k) 1 or equivalently k k NL , this perturbation theory is manifestly convergent. The effective theory differs from the so-called standard perturbation theory (SPT), and relatives (see for example [3,4] or [5]), by additional terms in the equations of motion for the overdensities that parameterize relevant short-distance physics. Approximately, these can be thought of as corrections to the fluid equations of motion in the form of speed of sound, viscosity, and stochastic pressure.…”

Section: Introductionmentioning

confidence: 99%

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The Effective Field Theory of Large Scale Structures at two loops

Carrasco

Foreman

Green

et al. 2014

J. Cosmol. Astropart. Phys.

208

499

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Large scale structure surveys promise to be the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbation theory for the weakly non-linear regime of dark matter, where correlation functions are computed in an expansion of the wavenumber k of a mode over the wavenumber associated with the non-linear scale k NL . Since most of the information is contained at high wavenumbers, it is necessary to compute higher order corrections to correlation functions. After the one-loop correction to the matter power spectrum, we estimate that the next leading one is the two-loop contribution, which we compute here. At this order in k/k NL , there is only one counterterm in the EFTofLSS that must be included, though this term contributes both at tree-level and in several one-loop diagrams. We also discuss correlation functions involving the velocity and momentum fields. We find that the EFTofLSS prediction at two loops matches to percent accuracy the non-linear matter power spectrum at redshift zero up to k ∼ 0.6 h Mpc −1 , requiring just one unknown coefficient that needs to be fit to observations. Given that Standard Perturbation Theory stops converging at redshift zero at k ∼ 0.1 h Mpc −1 , our results demonstrate the possibility of accessing a factor of order 200 more dark matter quasi-linear modes than naively expected. If the remaining observational challenges to accessing these modes can be addressed with similar success, our results show that there is tremendous potential for large scale structure surveys to explore the primordial universe.

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Section: Dimensional Analysis For the Real Universementioning

confidence: 99%

Section: Predictions For Correlation Functions Involving Momentummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Effective Field Theory of Large Scale Structures at two loops

Carrasco

Foreman

Green

et al. 2014

J. Cosmol. Astropart. Phys.

208

499

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“…, and m 0, and that all depend on galaxy type T. The first term is composed of two pieces: in the first piece, we have modeled the damping of BAOs using a Gaussian as derived in [37,38] for the dark matter case; for the second piece, we have added a k-dependent boost that models the power added by mode-mode coupling and nonlinear bias. Our simple power-law form (with two parameters A 2 , m) is meant to describe this effect over a restricted range of scales.…”

Section: E a Necessary Modelmentioning

confidence: 99%

“…Although the effect in the power is rather well known and has been observed in recent numerical simulations of CDM spectra [4,43,46,47], our results constitute a rather precise measurement of this effect, with realistic errors drawn from the ensemble. A complete assessment of the damping of linear features such as BAOs is done by studying the propagator [37,38] rather than the power spectrum. See [28] for further discussion on this.…”

Section: B Mass Halo and Halo-mass Power Spectramentioning

confidence: 99%

Scale dependence of halo and galaxy bias: Effects in real space

2007

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We examine the scale dependence of dark matter halo and galaxy clustering on very large scales (0:01 < k h Mpc ÿ1 < 0:15), due to nonlinear effects from dynamics and halo bias. We pursue a two line offensive: high-resolution numerical simulations are used to establish some old and some new results, and an analytic model is developed to understand their origins. Our simulations show: (i) that the z 0 dark matter power spectrum is suppressed relative to linear theory by 5% on scales 0:05 < k h Mpc ÿ1 < 0:075; (ii) that, indeed, halo bias is nonlinear over the scales we probe and that the scale dependence is a strong function of halo mass. High mass haloes show no suppression of power on scales k < 0:07 h Mpc ÿ1 , and only show amplification on smaller scales, whereas low mass haloes show strong, 5%-10%, suppression over the range 0:05 < k h Mpc ÿ1 < 0:15. These results were primarily established through the use of the cross-power spectrum of dark matter and haloes, which circumvents the thorny issue of shot-noise correction. The halo-halo power spectrum, however, is highly sensitive to the shot-noise correction; we show that halo exclusion effects make this sub-Poissonian and a new correction is presented. Our results have special relevance for studies of the baryon acoustic oscillation features in the halo power spectra. Nonlinear mode-mode coupling: (i) damps these features on progressively larger scales as halo mass increases; (ii) produces small shifts in the positions of the peaks and troughs which depend on halo mass. We show that these effects on halo clustering are important over the redshift range relevant to such studies 0 < z < 2 , and so will need to be accounted for when extracting information from precision measurements of galaxy clustering. Our analytic model is described in the language of the ''halo model.'' The halo-halo clustering term is propagated into the nonlinear regime using ''1-loop'' perturbation theory and a nonlinear halo bias model. Galaxies are then inserted into haloes through the halo occupation distribution. We show that, with nonlinear bias parameters derived from simulations, this model produces predictions that are qualitatively in agreement with our numerical results. We then use it to show that the power spectra of red and blue galaxies depend differently on scale, thus underscoring the fact that proper modeling of nonlinear bias parameters will be crucial to derive reliable cosmological constraints. In addition to showing that the bias on very large scales is not simply linear, the model also shows that the halo-halo and halo-dark matter spectra do not measure precisely the same thing. This complicates interpretation of clustering in terms of the stochasticity of bias. However, because the shotnoise correction is nontrivial, evidence for this in the simulations is marginal.

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Cosmic Structure Formation with Kinetic Field Theory

et al. 2019

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Kinetic Field Theory (KFT) is a statistical field theory for an ensemble of point-like classical particles in or out of equilibrium. We review its application to cosmological structure formation. Beginning with the construction of the generating functional of the theory, we describe in detail how the theory needs to be adapted to reflect the expanding spatial background and the homogeneous and isotropic, correlated initial conditions for cosmic structures. Based on the generating functional, we develop three main approaches to non-linear, late-time cosmic structures, which rest either on the Taylor expansion of an interaction operator, suitable averaging procedures for the interaction term, or a resummation of perturbation terms. We show how an analytic, parameterfree equation for the non-linear cosmic power spectrum can be derived.We explain how the theory can be used to derive the density profile of gravitationally bound structures and use it to derive power spectra of cosmic velocity densities. We further clarify how KFT relates to the BBGKY hierarchy. We then proceed to apply kinetic field theory to fluids, introduce a reformulation of KFT in terms of macroscopic quantities which leads to a resummation scheme, and use this to describe mixtures of gas and dark matter. We discuss how KFT can be applied to study cosmic structure formation with modified theories of gravity. As an example for an application to a noncosmological particle ensemble, we show results on the spatial correlation function of cold Rydberg atoms derived from KFT.

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Renormalized cosmological perturbation theory

Cited by 570 publications

References 35 publications

The Effective Field Theory of Large Scale Structures at two loops

The Effective Field Theory of Large Scale Structures at two loops

Scale dependence of halo and galaxy bias: Effects in real space

Cosmic Structure Formation with Kinetic Field Theory

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