Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum - INSPIRE

DataBETA

Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum

Yonadav Barry Ginat
(
- Oxford U., Theor. Phys. and
- Oxford U.
)
,
Michael L. Nastac
(
)
,
Robert J. Ewart
(
)
,
Sara Konrad
(
- U. Heidelberg, ITP
)
,
Matthias Bartelmann
(
- U. Heidelberg, ITP
)

Jan 2, 2025

22 pages

e-Print:

2501.01524 [astro-ph.CO]

View in:

ADS Abstract Service

reference search0 citations

Citations per year

0 Citations

Abstract: (arXiv)

The matter power spectrum,

P(k)

, is one of the fundamental quantities in the study of large-scale structure in cosmology. Here, we study its small-scale asymptotic limit, and show that for cold dark matter in

d

spatial dimensions,

P(k)

has a universal

k^{-d}

asymptotic scaling with the wave-number

k

, for

k \gg k_{\rm nl}

, where

k_{\rm nl}^{-1}

denotes the length scale at which non-linearities in gravitational interactions become important. We propose a theoretical explanation for this scaling, based on a non-perturbative analysis of the system's phase-space structure. Gravitational collapse is shown to drive a turbulent phase-space flow of the quadratic Casimir invariant, where the linear and non-linear time scales are balanced, and this balance dictates the

k

dependence of the power spectrum. A parallel is drawn to Batchelor turbulence in hydrodynamics, where large scales mix smaller ones via tidal interactions. The

k^{-d}

scaling is also derived by expressing

P(k)

as a phase-space integral in the framework of kinetic field theory, which is analysed by the saddle-point method; the dominant critical points of this integral are precisely those where the time scales are balanced. The coldness of the dark-matter distribution function -- its non-vanishing only on a

d

-dimensional sub-manifold of phase-space -- underpins both approaches. The theory is accompanied by

1\mathrm{D}

Vlasov--Poisson simulations, which confirm it.

Note:

Submitted, comments welcome

References(74)

Figures(8)

[1]

The Large-Scale Structure of the Universe (Princeton University Press, Princeton, N.J

P.J.E. Peebles

[2]

Modern Cosmology

Scott Dodelson
(
- Fermilab and
- Chicago U.
)

- Amsterdam, Netherlands: Academic Pr. (2003) 440 p

[3]

Large-Scale Galaxy Bias

Vincent Desjacques
(
- Geneva U., CAP and
- Geneva U., Dept. Theor. Phys. and
- Technion
)
,
Donghui Jeong
(
)
,
Fabian Schmidt
(
- Garching, Max Planck Inst.
)

- Phys.Rept. 733 (2018) 1-193,
- Physics Reports Volume 733, 1-193 (28 February 2018)
•
e-Print:
- 1611.09787
•
DOI:
- 10.1016/j.physrep.2017.12.002

[4]

Planck 2018 results. VI. Cosmological parameters

Planck

Collaboration

•

N. Aghanim
(
- Orsay, IAS
)

et al.

- Astron.Astrophys. 641 (2020) A6,
- Astron.Astrophys. 652 (2021) C4 (erratum)
•
e-Print:
- 1807.06209
•
DOI:
- 10.1051/0004-6361/201833910

[5]

Separating the early universe from the late universe: Cosmological parameter estimation beyond the black box

Max Tegmark
(
- Pennsylvania U.
)
,
Matias Zaldarriaga
(
- New York U. and
- Princeton, Inst. Advanced Study
)

- Phys.Rev.D 66 (2002) 103508
•
e-Print:
- astro-ph/0207047
•
DOI:
- 10.1103/PhysRevD.66.103508

[6]

Snowmass white paper: Effective field theories in cosmology

Giovanni Cabass
(
- Princeton, Inst. Advanced Study
)
,
Mikhail M. Ivanov
(
- Princeton, Inst. Advanced Study
)
,
Matthew Lewandowski
(
- Northwestern U.
)
,
Mehrdad Mirbabayi
(
- ICTP, Trieste
)
,
Marko Simonović
(
- CERN
)

- Phys.Dark Univ. 40 (2023) 101193
•
e-Print:
- 2203.08232
•
DOI:
- 10.1016/j.dark.2023.101193

[7]

Gravitation

D. Heggie
,
P. Hut

•
DOI:
- 10.1017/CBO9781139164535

[8]

Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

- Astrophys.J.Lett. 374 (1991) L1
•
DOI:
- 10.1086/186057

[9]

Multiple-Scales Approach to The Averaging Problem in Cosmology

Yonadav Barry Ginat
(
- Technion
)

- JCAP 02 (2021) 049
•
e-Print:
- 2005.03026
•
DOI:
- 10.1088/1475-7516/2021/02/049

[10]

Cosmological Non-Linearities as an Effective Fluid

- JCAP 07 (2012) 051
•
e-Print:
- 1004.2488
•
DOI:
- 10.1088/1475-7516/2012/07/051

[11]

Effective Field Theory of Large-Scale Structure

Tobias Baldauf

- Les Houches Lect.Notes 108 (2020)
•
DOI:
- 10.1093/oso/9780198855743.003.0007

[12]

Effective Field Theory for Large-Scale Structure

Mikhail M. Ivanov
(
- Princeton, Inst. Advanced Study
)

[13]

First results from the IllustrisTNG simulations: matter and galaxy clustering

et al.

- Mon.Not.Roy.Astron.Soc. 475 (2018) 1, 676-698
•
e-Print:
- 1707.03397
•
DOI:
- 10.1093/mnras/stx3304

[14]

Post-collapse perturbation theory in 1D cosmology – beyond shell-crossing

- Mon.Not.Roy.Astron.Soc. 470 (2017) 4, 4858-4884
•
e-Print:
- 1701.09088
•
DOI:
- 10.1093/mnras/stx1501

[15]

Phase-space structure analysis of self-gravitating collisionless spherical systems

A. Halle
,
S. Colombi
,
S. Peirani

- Astron.Astrophys. 621 (2019) A8
•
e-Print:
- 1701.01384
•
DOI:
- 10.1051/0004-6361/201833460

[16]

Asymptotic expansions for Large Scale Structure

Shi-Fan Chen
(
- UC, Berkeley
)
,
Massimo Pietroni
(
- INFN, Padua and
- U. Parma (main)
)

- JCAP 06 (2020) 033
•
e-Print:
- 2002.11357
•
DOI:
- 10.1088/1475-7516/2020/06/033

[17]

Collisional relaxation in stellar systems

I.H. Gilbert

- Astrophys.J. 152 (1968) 1043
•
DOI:
- 10.1086/149616

[18]

Kinetic theory of long-range interacting systems with angle-action variables and collective effects

P.-H. Chavanis

- Physica A 391 (2012) 3680
•
e-Print:
- 1107.1475
•
DOI:
- 10.1016/j.physa.2012.02.019

[19]

A mean field limit for the Vlasov-Poisson system

D. Lazarovici
,
P. Pickl

- Arch.Ration.Mech.Anal. 225 (2017) 1201
•
DOI:
- 10.1007/s00205-017-1125-0

[20]

Cosmological Vlasov–Poisson equations for dark matter: Recent developments and connections to selected plasma problems

Cornelius Rampf
(
- Vienna U., Dept. Math. and
- Vienna U.
)

- Rev.Mod.Plasma Phys. 5 (2021) 1, 10
•
e-Print:
- 2110.06265
•
DOI:
- 10.1007/s41614-021-00055-z

[21]

The power spectrum of SUSY - CDM on sub-galactic scales

- Mon.Not.Roy.Astron.Soc. 353 (2004) L23
•
e-Print:
- astro-ph/0309621
•
DOI:
- 10.1111/j.1365-2966.2004.08232.x

[22]

The Small-scale power spectrum of cold dark matter

- Phys.Rev.D 71 (2005) 103520
•
e-Print:
- astro-ph/0504112
•
DOI:
- 10.1103/PhysRevD.71.103520

[23]

Constraints on dark-matter properties from large-scale structure

- Phys.Rev.D 94 (2016) 2, 023510
•
e-Print:
- 1604.05701
•
DOI:
- 10.1103/PhysRevD.94.023510

[24]

Constraining the Properties of Dark Matter with Observations of the Cosmic Microwave Background

- Astrophys.J. 830 (2016) 2, 155
•
e-Print:
- 1601.05097
•
DOI:
- 10.3847/0004-637X/830/2/155

[25]

Warm dark matter chills out: constraints on the halo mass function and the free-streaming length of dark matter with eight quadruple-image strong gravitational lenses

et al.

- Mon.Not.Roy.Astron.Soc. 491 (2020) 4, 6077-6101
•
e-Print:
- 1908.06983
•
DOI:
- 10.1093/mnras/stz3480

1-25 of 74
1
2
3
25 / page