Kinetic field theory: effects of momentum correlations on the cosmic density-fluctuation power spectrum

Bartelmann, Matthias; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Dombrowski, Johannes; Mildenberger, Julius

doi:10.1088/1367-2630/aa7e6f

Cited by 29 publications

(107 citation statements)

References 25 publications

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“…We have not explained yet how [ ] Z L, 0 0 can be treated. We have shown in [2] that, by introducing the internal wave vectors  k ab for a>b and a=3, ..., l, the two-particle term can be factorized into a single, numerically tractable integral of standard form:…”

Section: Factorizationmentioning

confidence: 99%

“…Crucially, the function  jk can be quickly evaluated numerically using e.g. a Levin collocation scheme [2,[11][12][13]].…”

Section: Factorizationmentioning

confidence: 99%

“…For > t t 2 1 the left hand-side has to vanish due to causality. Using that the operator  ( ) t j 1, 1 is equivalent to a regular time derivative for the auto-correlation, we arrive at the FDR (55):…”

Section: Fluctuation-dissipation Relations From the Time-reversal Symmentioning

confidence: 99%

“…Recently, Bartelmann et al [1][2][3] developed a Kinetic Field Theory (KFT) to treat cosmic structure formation based on methods introduced first by Das and Mazenko in [4][5][6][7] and structurally similar to non-equilibrium quantum field theory. This formalism mirrors the approach of N-body simulations following particles in phase space and, thus, avoiding difficulties with shell crossing ubiquitous in conventional approaches to cosmic structure formation.…”

Section: Introductionmentioning

confidence: 99%

“…This article begins with an introduction into KFT in section 2, which summarizes the main results from the previous works [1][2][3] and introduces our notation and methods. We then study in section 3 the time derivative of the non-linear density power spectrum and discuss FDRs in section 4.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic field theory: cosmic structure formation and fluctuation-dissipation relations

2018

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Building upon the recently developed formalism of Kinetic Field Theory (KFT) for cosmic structure formation by Bartelmann et al, we investigate a kinematic relationship between diffusion and gravitational interactions in cosmic structure formation. In the first part of this work we explain how the process of structure formation in KFT can be separated into three processes, particle diffusion, the accumulation of structure due to initial momentum correlations and interactions relative to the inertial motion of particles. We study these processes by examining the time derivative of the nonlinear density power spectrum in the Born approximation. We observe that diffusion and accumulation are delicately balanced because of the Gaussian form of the initial conditions, and that the net diffusion, resulting from adding these two counteracting contributions, approaches the contributions from the interactions in amplitude over time. This hints at a kinematic relation between diffusion and interactions in KFT. Indeed, in the second part, we show that the response of the system to arbitrary gradient forces is directly related to the evolution of particle diffusion in the form of kinematic fluctuation-dissipation relations (FDRs). This result is independent of the interaction potential. We show that this relationship roots in a time-reversal symmetry of the underlying generating functional. Furthermore, our studies demonstrate how FDRs originating from purely kinematic arguments can be used in theories far from equilibrium.

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Section: Factorizationmentioning

confidence: 99%

“…Crucially, the function  jk can be quickly evaluated numerically using e.g. a Levin collocation scheme [2,[11][12][13]].…”

Section: Factorizationmentioning

confidence: 99%

Section: Fluctuation-dissipation Relations From the Time-reversal Symmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kinetic field theory: cosmic structure formation and fluctuation-dissipation relations

2018

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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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Kinetic field theory for cosmic structure formation

Konrad

Bartelmann

2022

Riv. Nuovo Cim.

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We apply kinetic field theory to non-linear cosmic structure formation. Kinetic field theory decomposes the cosmic density field into particles and follows their trajectories through phase space. We assume that initial particle momenta are drawn from a Gaussian random field. We place particular emphasis on the late-time, asymptotic behaviour on small spatial scales of low-order statistical measures for the distribution of particles in configuration and velocity space. Our main result is that the power spectra for density and velocity fluctuations in ensembles of particles freely streaming along Zel’dovich trajectories asymptotically fall off with wave number k like $$k^{-3}$$ k - 3 for $$k\rightarrow \infty $$ k → ∞ , irrespective of the cosmological model and the type of dark matter assumed, with the exponent set only by the number of spatial dimensions. This conclusion remains valid for density-fluctuation power spectra if particle interactions are taken into account in a mean-field approximation. We also show that the bispectrum of freely streaming particles falls off asymptotically like $$k^{-11/2}$$ k - 11 / 2 under the same general conditions.

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Kinetic field theory: effects of momentum correlations on the cosmic density-fluctuation power spectrum

Cited by 29 publications

References 25 publications

Kinetic field theory: cosmic structure formation and fluctuation-dissipation relations

Kinetic field theory: cosmic structure formation and fluctuation-dissipation relations

Cosmic Structure Formation with Kinetic Field Theory

Kinetic field theory for cosmic structure formation

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