Math 2.0

Astronomy and astrophysics Definition

Structure formation

Builds on Scale factorFriedmann equationsJeans instabilityMatter power spectrum

Definition

Consider an expanding universe with scale factor a(t)a(t) governed by the Friedmann equations, with mean matter density ρˉ(t)\bar\rho(t). The density contrast at comoving position xx is δ(x,t)=ρ(x,t)−ρˉ(t)ρˉ(t).\delta(x, t) = \frac{\rho(x, t) - \bar\rho(t)}{\bar\rho(t)}. Structure formation is the evolution of δ\delta under gravity. It leads from a nearly Gaussian random field with ∣δ∣≪1\abs{\delta} \ll 1 at early times to bound objects with δ≫1\delta \gg 1, such as halos and clusters. It has a linear regime, ∣δ∣≪1\abs{\delta} \ll 1, in which each Fourier mode grows independently, and a nonlinear regime.

Remarks

The statistics of δ\delta in the linear regime are given by the matter power spectrum. The growth is driven by the Jeans instability, slowed by the expansion: in a universe of matter only, linear perturbations grow as δ∝a\delta \propto a.

Example: a region with δ=10−3\delta = 10^{-3} at a=10−3a = 10^{-3} in such a universe reaches δ≈1\delta \approx 1 near a=1a = 1 in linear theory, and then goes nonlinear and collapses.

Non-example: a perfectly homogeneous universe has δ≡0\delta \equiv 0 at all times; there is no structure to grow.

The nonlinear regime is studied with N-body simulations and with approximate models such as spherical collapse.

Reading path

To understand this page from the ground up, read these 17 pages in order. The foundations come first.

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Cosmological constant, concept, no evidence levelCosmological constantconceptCosmological principle, concept, no evidence levelCosmological principleconceptDispersion relation, concept, no evidence levelDispersion relationconceptEinstein field equations, concept, no evidence levelEinstein field equati…conceptEuler equations, concept, no evidence levelEuler equationsconceptJeans length, concept, no evidence levelJeans lengthconceptMatter power spectrum, concept, no evidence levelMatter power spectrumconceptPerfect fluid, concept, no evidence levelPerfect fluidconceptPoisson's equation, concept, no evidence levelPoisson's equationconceptScale factor, concept, no evidence levelScale factorconceptSpace form, concept, no evidence levelSpace formconceptSpacetime, concept, no evidence levelSpacetimeconceptSpeed of sound, concept, no evidence levelSpeed of soundconceptJeans instability, statement, no evidence levelJeans instabilitystatementFriedmann–Lemaître–Robertson–Walker metric, example, no evidence levelFriedmann–Lemaître–Ro…exampleFriedmann equations, statement, no evidence levelFriedmann equationsstatementStructure formation, definition, no evidence levelStructure formationdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Cosmological constant concept
  2. Cosmological principle concept
  3. Dispersion relation concept
  4. Einstein field equations concept
  5. Euler equations concept
  6. Jeans length concept
  7. Matter power spectrum concept
  8. Perfect fluid concept
  9. Poisson's equation concept
  10. Scale factor concept
  11. Space form concept
  12. Spacetime concept
  13. Speed of sound concept
  14. Jeans instability statement
  15. Friedmann–Lemaître–Robertson–Walker metric example
  16. Friedmann equations statement
  17. Structure formation definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Structure_formation
About this page
TagTHQA4B3206
URIm2://THQA4B3206
Kinddefinition
WritingW0 stub
MSC85A40
DefinesStructure formation
UsesScale factor, Friedmann equations, Jeans instability, Matter power spectrum
Changed3 November 2026

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