History of cosmic structure formation

How did seed fluctuations grow into today's cosmic structures such as galaxies and galaxy clusters?

The growth of seed fluctuations into cosmic structure can be summarised into three main phases:

1. Between inflation and the release of the cosmic microwave background
2. Between the release of the cosmic microwave background and the formation of the first stars and galaxies
3. After the formation of the first stars and galaxies

Between inflation and the release of the cosmic microwave background (t <1 sec to t =380,000 years)

After the end of inflation, the Universe consisted of a more or less uniform bath of fundamental particles, like quarks, electrons and their anti-particles. There were also neutrinos, photons (the particles of light) and dark matter particles, an unknown type of massive particle that does not interact with photons and is therefore dark (as it does not emit light). At this time there was slightly more matter than anti-matter, but as the particles collided with their anti-particles they annihilated, leaving the Universe dominated by particles, and anti-matter disappeared. Quarks then teamed up in trios, forming protons or neutrons – the constituents of atomic nuclei as we know them today. This all happened within the first second after the Big Bang. About three minutes after the Big Bang, protons and neutrons had combined to form the nuclei of hydrogen and helium.

The density and temperature of particles in the early Universe were extremely high, and collisions between the particles were very frequent. Cosmologists refer to this by saying that ordinary matter (such as electrons, protons, neutrons and the few atomic nuclei that had formed by then) was tightly coupled to the photons. Because of these frequent interactions, photons could not travel freely: the Universe was opaque. Besides, ordinary matter is subject to gravity, and ideally any denser region – such as the seed fluctuations that were present at the end of inflation – would draw more matter from their surroundings, growing denser and more massive. However, ordinary matter at this epoch was coupled to the photons, and the radiation pressure of photons pushes away any concentration of matter that may be created under the effect of gravity. This phenomenon prevents any fluctuations in the distribution of ordinary matter to grow denser as long as matter is coupled to the photons.

At the same time, dark matter particles were not bound to the photons, since the two species do not interact with one another. This type of dark matter particle is also referred to as cold dark matter because the velocity of these particles is much lower than the speed of light. Hence, fluctuations in the distribution of cold dark matter can grow denser and more massive even before the release of the cosmic microwave background.

Astronomers also refer to hot dark matter, or neutrinos – particles with a very small mass and no electric charge that travel nearly at the speed of light. In the first second of the Universe, neutrinos were coupled to the photons, but these two types of particles decoupled immediately after. Since they do not interact with light during most of the Universe's history, neutrinos can be considered as a type of dark matter, and since their velocity is close to the speed of light, they are regarded as hot dark matter. Fluctuations in the distribution of hot dark matter can grow denser and more massive, but due to their high velocity, these particles tend to dissipate and their fluctuations are damped on small scales so, effectively, only fluctuations on intermediate and large scales can grow.

The growth of primordial fluctuations in hot and cold dark matter give rise to two completely different distributions of cosmic structure. In hot dark matter models, the first structures to form are the most massive, that subsequently fragment into smaller and smaller structures. This has been discarded on the basis of observations of galaxies in the early Universe: since the first objects that are seen to emerge in cosmic history have low mass, and they gradually evolve into more massive structures, cosmologists have established that the bulk of dark matter in the Universe is cold. However, a small fraction of hot dark matter is present in the Universe as neutrinos. Depending on the mass of neutrinos (which has not been determined yet) the effect of hot dark matter can be more or less evident in the distribution of cosmic structure on different scales, since neutrinos tend to smooth out the formation of small-scale structures.

Between the release of the cosmic microwave background and the formation of the first stars and galaxies (t = 380,000 years to t = a few hundred million years)

About 380,000 years after the Big Bang, the Universe had expanded enough so that its density was much lower than at earlier epochs. Likewise, the temperature of the Universe had cooled down from the billions of Kelvin of the first few minutes and had reached about 3000 Kelvin. Protons and electrons could finally combine to form atoms of neutral hydrogen. Electrons disappeared from the view of photons and these two species decoupled from one another. This marked the beginning of the period known as the Dark Ages – a name arising from the fact that there were no individual sources of light, like stars, only clouds of neutral hydrogen.

The decoupling had two effects: photons were free to propagate across the Universe, which was now largely transparent, and which we observe as the cosmic microwave background (CMB); on the other hand, ordinary matter particles were free to assemble under the effect of gravity. From this moment on, ordinary and dark matter could both react to gravity: denser concentrations of matter (both ordinary and dark) grew denser and more massive. Since dark matter particles had already created a network of dense and empty structure, ordinary matter particles could feel the gravitational attraction from the densest concentrations of dark matter and fall toward them. But ordinary matter could also get rid of energy quite effectively by heating up and emitting radiation, which caused it to sink even further into the already existing regions of high matter density. These processes gave rise to a highly sub-structured network of sheets and filaments of ordinary and dark matter known as the cosmic web, which constitutes the skeleton supporting the later emergence of stars and galaxies. Eventually the densest concentrations gave rise to the first stars, leading to the end of the Dark Ages.

After the formation of the first stars and galaxies (t = a few hundred million years to t = now)

A few hundred million years after the Big Bang, the distribution of matter in the Universe had produced very dense knots at the intersections of the sheets and filaments that make up the cosmic web. In these knots, the density of ordinary matter was so high that the formation of stars and galaxies became possible. Eventually the first stars and galaxies sparked into existence and light could escape from them, revealing the distant Universe to telescopes today.

The first stars were formed almost exclusively out of hydrogen and helium and are believed to have been extremely massive (about 100 times the mass of the Sun or more) and to have lived very short lives, exploding soon after their formation as supernovae and releasing their material in the surroundings, triggering the birth of new stellar generations. Later generations included other elements formed in the nuclear furnace of previous stars, and their masses were typically smaller. The first generation of stars formed in relatively low-mass galaxies. Massive galaxies, and even more massive structures such as galaxy clusters, formed later.

How did the formation of structure effect the cosmic microwave background?
The birth of the first stars and galaxies had an interesting effect on the cosmic microwave background (CMB) photons. Ultraviolet radiation released by these objects ionised hydrogen atoms, turning them back into protons and electrons. This created a series of expanding bubbles of ionised gas – a bit like the holes in Swiss cheese – and within a few hundred million years these bubbles had merged and the entire Universe was ionised again, a period of time termed reionisation.

The CMB photons were affected by the reionisation; they were scattered off the free electrons in the reionised Universe, washing out some of the primordial fluctuations in the CMB as we observe it today. Since this happened when the Universe was already mature and had reached a substantial size, the effect of reionisation can be detected in the fluctuations of the CMB on large scales. This effect is expressed in terms of the ‘opacity’, which describes the average density of free electrons that are present along the line of sight between an observer (in this case, the telescope on board Planck) and the CMB. This parameter also provides a tool to estimate when the first stars formed.

How is the history of cosmic structure encoded in the cosmic microwave background and power spectrum?
The variations in the density of matter at the time when the cosmic microwave background (CMB) formed derive from the seed fluctuations that were produced at the end of inflation and can be deciphered by looking at the power spectrum for cosmic structure in the Universe at a range of scales.

At scales smaller than about one degree – or twice the size of the full Moon on the sky – the graph shows the imprint and oscillation pattern of sound waves that were present in the fluid of ordinary matter and radiation in the very early Universe, before the CMB was released. At this epoch, ordinary matter was tightly coupled to the photons, and the radiation pressure of photons pushed away any concentration of matter that might have been created under the effect of gravity.

The interplay between gravity, which pulled together the fluid of matter and radiation, and the radiation pressure, which pushed it away, caused a series of rhythmical compressions and rarefactions everywhere in the fluid. This results in the pattern of sound waves that is visible in the central part of the power spectrum graph. Since gravity is caused by both dark and ordinary matter particles, but the radiation pressure of photons is only experienced by ordinary matter (because dark matter particles are not coupled to photons), the shape of these oscillations contains information about the amount of ordinary matter relative to the amount of dark matter. As dark matter was not bound to the photons, any concentration of dark matter could grow denser and denser even before the release of the CMB. The relative contribution of ordinary matter particles (also referred to as baryons) to the overall cosmic budget is expressed in terms of the 'Omega_b' parameter, where b stands for baryons, and the relative contribution of cold dark matter particles is expressed in terms of the 'Omega_c' parameter, where c stands for cold. The ‘cold’ in cold dark matter refers to the low speed of these particles (‘warm’ dark matter particles move at higher speed and ‘hot’ dark matter particles move at the speed of light).
While gravity pulls matter together to form structures, the expansion of the Universe may counteract this effect and hamper the formation of cosmic structure. For this reason, the amount of fluctuations in the Universe depends also on the speed of cosmic expansion, and this quantity can be extracted from the shape of the oscillations in the power spectrum of the CMB. The speed of the Universe is expressed in terms of the Hubble constant, H_0, which quantifies the expansion of the Universe at present time.

What does the cosmic microwave background tell us about the overall 'shape' of the Universe?
The CMB holds clues to the nature and distribution of structure in the Universe, and the average density of this matter plays a key role in determining the geometry of the Universe. The geometry of the Universe can take on one of three shapes: it can be curved like the surface of a ball and finite in extent (positively curved); curved like a saddle and infinite in extent (negatively curved), or it can be flat and infinite. The geometry and density of the Universe are related in such a way that, if the average density of matter in the Universe is found to be less than the so-called critical density (roughly equal to 6 hydrogen atoms per cubic metre) the Universe is open and infinite. If the density is greater than the critical density the Universe is closed and finite. If the density just equals the critical density, the Universe is flat.

Cosmologists study the relative sizes of the oscillations of the fluid of matter and radiation at the time the CMB was released to learn more about the shape of the Universe. The oscillations translate into regions of higher and lower temperature on the CMB map, and contain information about the amount of particles present. More specifically, the shape of the Universe can be determined by looking at where the first of these oscillations appears in the power spectrum.

The location of the first oscillation corresponds to a specific size in the early Universe called the sound horizon – the maximum distance that a sound wave could have crossed from the Big Bang until the time of the CMB release. To cosmologists, the sound horizon works like a standard measure of known length. By measuring its length in the temperature fluctuations of the CMB, it is possible to determine if the Universe is flat or curved. This is expressed in terms of the parameter 'Omega_K' and is equal to zero for exactly flat space.