User:TychosElk/sandbox

= Structure formation =

The ΛCDM model provides quantitative predictions for structure formation over the history of the Universe. The initial small density fluctuations at very early times are modelled by a power-law (consistent with the prediction of cosmic inflation, which is specified by the two parameters A and $$n_S$$ below. These density fluctuations evolve differently for dark matter, baryonic matter, photons and neutrinos, since the photons are strongly coupled to baryons, but dark matter is uncoupled, while neutrinos free-stream at relativistic speeds. Since the density perturbations are small, linear perturbation theory can be applied; this leads to a hierarchy of coupled differential equations. These cannot be solved analytically, though approximate solutions can be derived; but the equations can be solved to high accuracy with sophisticated modern computer codes such as CMBFast, CLASS and CAMB; these codes give predictions for the observable CMB anisotropy and matter power spectrum for any input set of cosmological parameters, in a run-time of tens of seconds per parameter-set on a desktop computer.

After recombination at $$ z_{rec} \approx 1090 $$, about 375,000 years after the Big Bang, there then follows the so-called  Dark Ages for the next 100-200 million years; this era is quite simple theoretically, since matter dominated the energy density, the CMB did not interact with neutral atoms and propagated freely, and density perturbations were small and simply grew in amplitude proportional to the cosmic scale factor. During the Dark Ages there were no dense structures such as galaxies or stars. There are currently no direct observations from the Dark Ages, though there is the future possibility of measuring very weak 21 cm emission from neutral hydrogen, now highly redshifted to few-metre radio wavelengths which are challenging to observe due to Earth's ionosphere.

At around redshift of 40 to 20, small overdense regions of dark matter become dense enough to become non-linear and then collapse into gravitationally bound blobs of dark matter, known as "dark halos"; from this point on, analytic calculations start to break down and the growth of cosmic structure is calculated with large N-body simulations, which evolve the positions and velocities of billions of simulated matter particles in supercomputers. Simulations show that the dark-matter halos are well approximated by slightly non-spherical blobs with a density profile fitted by the NFW profile. Small halos then grew and merged into larger halos, and some of the resulting halos became large enough for baryons to cool inside them, contract further and form the first luminous galaxies and stars, at an estimated redshift between 20 to 15. This era is known as "First Light" or "cosmic dawn", and is slightly beyond the reach of current telescopes such as Hubble Space Telescope, but is likely to be probed by observations with the JWST in the near future. As the abundance of small galaxies increased, the UV light from their young stars became intense enough to ionize the surrounding neutral hydrogen, and the ionized bubbles grew and eventually overlapped, leading to cosmic reionization, at a redshift measured at 8--9 by the Planck spacecraft.

After reionization, galaxies continued to become more numerous and more massive, leading to an era of peak star formation rate (per comoving volume) at redshifts between 3 to 1.5, known as "cosmic noon"; it is well established that the abundance of quasars also peaked around this era. Large-scale structures such as clusters and superclusters also developed during this era, while large-scale underdensities expanded into giant voids, forming the "cosmic web" of structure observed in the recent universe by large galaxy redshift surveys. From redshift of 1 to the present day, observations show there has been a rather steep decline in the cosmic star-formation rate.

The large N-body simulations provide precise predictions for statistics such as the galaxy power spectrum and the abundance of galaxy clusters, which are in good agreement with modern observations. Modern simulations also incorporate hydrodynamic modelling to predict the structure of individual galaxies, though these are considerably more challenging and require various approximations.