Cosmology and astrophysics

Structure formation and galaxies

Tiny density fluctuations in the early universe grow under gravity; dark matter helps form gravitational wells in which gas gathers into galaxies.

Tiny density fluctuations in the early universe grow under gravity; dark matter helps form gravitational wells in which gas gathers into galaxies.

Model and observations

δ is the density contrast. Gravity amplifies regions slightly denser than average; gas can cool and fall into dark-matter halos, where stars form.

A perturbation with contrast $\delta=(\rho-\bar\rho)/\bar\rho$ grows linearly while $|\delta|\ll1$. During matter domination, sub-horizon perturbations grow approximately with the scale factor $a$; once $\delta$ becomes order unity, linear theory fails and overdense regions collapse into halos. Halos assemble hierarchically, while baryonic gas radiates energy, cools, and forms stars. $N$-body simulations follow collisionless matter, whereas hydrodynamical models must also represent cooling and stellar feedback.

CMB temperature fluctuations of only about $10^{-5}$ reveal the initial amplitude of primordial perturbations; gravitational lensing and galaxy surveys test their later growth. The matter power spectrum contains a turnover and baryon acoustic features, so halo masses are not distributed randomly. Comparing observed structure with predictions jointly tests gravity, dark-matter candidates, and feedback from stars and black holes. A mismatch on small scales does not automatically falsify the standard model: selection bias, gas physics, and sub-grid simulation prescriptions must first be assessed.

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