The present day universe has large variations in density even on scales significantly larger than galaxies. For example, counting galaxies in Mpc3 volumes, we find tens of galaxies more massive than the Milky Way in the centres of rich clusters, but no galaxies to even lower masses in parts of voids. These density variations grew from fluctuations smaller than 1 part in 1010 in the early universe through gravitational collapse. The density fluctuations are often described by the power spectrum, here given by the dimensionless version Δ2(k) such that σ2 = ∫ Δ2(k) d ln k , where k is the wavenumber in an isotropic universe so that it does not depend on direction (the wavelength of the Fourier components is 2π/k), and σ is the standard deviation of the density relative to the mean density. Thus Δ2(k) represents the contribution to the variance of density fluctuations per ln k, i.e. around a given scale.
The movie below shows the evolution of the power spectra [the square root thereof, Δ(k)] for five different particle types (cold dark matter, baryons, photons, massless neutrinos, and neutrinos with mass) as a function of the scale given by the half wavelength of the fluctuations. This evolution is determined, starting from a power-law function as predicted by inflation, by accounting for gravity, distributions in particle energies, and interactions between the particles. This represent the linear theory which is accurate while Δ2(k) remains significantly smaller than unity. As the fluctuations approach unity, non-linear collapse occurs, which for galaxy formation requires more complex simulations.
Links: fluctuations-evolve.mp4 (as below if displayed); fluctuations-evolve2.mp4 (zoomed in version, 1 to 1000 Mpc, focus on acoustic oscillations); CAMB code distribution (Antony Lewis and Anthony Challinor). See notes below for more details of the animations.
Note on animations: the black dotted line shows the power-law function of the initial fluctuations (n=0.96); the black dashed line at the bottom shows the horizon scale; the right-hand panel shows various calculations for a universe with Hubble parameter h=0.68, ΩCDM,0=0.24, Ωb,0=0.05, Ων,0=0.01; the standard contribution of kinetic energy in neutrinos is assumed (0.69 of photon energy density); the dark energy contribution is black in the pie chart, of course. The arrows are to remind you that we should think of the fluctuations increasing (or decreasing) at fixed scale rather than the power spectrum moving sideways as it appears to.
Effects to look out for: tight coupling between baryons and photons until decoupling; the point of matter-energy equality in the pie chart; slow growth of CDM fluctuations below the horizon scale until matter dominates; the rapid catch up of baryons to CDM after decoupling; the point when neutrinos with mass become non relativistic.
Page written by Ivan Baldry.
Link: return to my cosmology links page.