signs, such as an alteration of X-ray luminosity, the existence of unusual jets, a disturbed morphology. It may well be possible in many cases to identify the host galaxy within the LISA position error box, which may be less than 10 arcminutes in size in favorable cases.

A gravitational-wave measurement would be a very desirable complement to other studies of the dark energy, because it needs no calibration: it would be independent of the assumptions of the cosmic distance ladder. It would therefore be an important check on the systematic errors of other methods.

12.4 P h y s i c a l co s m o l o g y : t h e e v o l u t i o n o f t h e u n i v e r s e w e o b s e r v e

The observations described in the last section confirm the reliability of using a generalrelativistic cosmological model with dark energy to describe the evolution of the universe, starting as far back as our observations can take us. During the last few decades, astrophysicists have developed a deep and rich understanding of how the universe we see, with all its structure and variety, evolved out of a homogeneous hot expanding plasma. The story is a fascinating one that we can only sketch here. But it is fair to say that there is now a consistent story that goes from the moment that protons and neutrons became identifiable particles right up to the formation of stars like our Sun and planets like our Earth. Many of the details are poorly understood, especially where observations are difficult to perform, but the physical framework for understanding them is not in doubt.

The expansion of the universe was accompanied by a general cooling off of its matter: photons have been redshifted, the random velocities of gas particles dropped, structures like galaxies and stars condensed out. The history of the universe is therefore a thermal history: instead of using cosmological time t or the scale factor R to mark different stages of evolution, we will use temperature, or equivalently energy, converting between them by E = kT. That brings us closer to the physics.

Our understanding of the history of the universe rests on our understanding of its physical laws, and these are tested up to energies of order 1 TeV in modern particle colliders. So our physical picture of the evolution of the universe can reliably start when the expanding plasma had that sort of energy.

Decoupling: forming the cosmic mic rowave background radiation

If we start at the present moment and go backwards, the matter energy density increases as the scale factor R decreases, but the dark energy density remains constant, so (unless the dark energy comes from some exotic physics) we can safely ignore the dark energy at early times. The density of ordinary matter (dark and baryonic) increases as R−3, while the energy density of the photons of the cosmic microwave background increases as R−4.

Since the energy density of the cosmic microwave background today is γ 10−5 and the matter density is m = 0.3, they will have been equal when the scale factor was a factor of 3 × 104 smaller than today. Since redshift and scale factor go together, this is the redshift when the expanding universe changed from radiation-dominated to matter dominated. At higher redshifts, the universe was radiation-dominated. The temperature was about 105K and the energy scale was about 10 eV. This happened about 3000 years after the Big Bang.

Now, this energy is near the ionization energy of hydrogen, which is 13.6 eV. This is an important number because hydrogen is the principal constituent of the baryonic matter. If the temperature is high enough to ionize hydrogen, the universe will be filled with a plasma that is opaque to electromagnetic radiation. Once hydrogen cools off enough to become neutral, the remaining photons in the universe will be able to move through it with a low probability of scattering. This moment of decoupling (also called recombination) defines the moment at which the cosmic microwave background radiation was created. This actually occurs at a rather smaller energy than 13.6 eV, since there is enough hydrogen to stop the photons even when only a small portion of it is ionized. The epoch of decoupling occurred at a temperature a bit below 1 eV, at a time when the universe was matter-dominated. The redshift was about 2000, and the time was about 4 × 105 years after the Big Bang.

Observations of the cosmic microwave background reveal that it has an almost perfect black-body spectrum with a temperature of T = 2.725K. But they also show that it has small but significant temperature irregularities, departures from strict homogeneity that are the harbingers of the formation of galaxy clusters and galaxies. A map of these is shown in Fig. 12.5. The temperature irregularities are of order 10−5 of the background temperature, and they are caused by irregularities in the matter distribution of the same relative size. Small as these may seem, numerical studies show that they are adequate to lead to all the structure we see today. Because the dominant form of matter is the dark matter, the density fluctuations that are seen in Fig. 12.5 and that led to galaxy formation were in its

A map of the small-scale temperature inhomogeneities of the cosmic microwave background,

Figure 12.5

made by the WMAP satellite (Spergel, et al, 2003). The range of fluctuations is ±200μK. Figure

distribution. Simulations show that only if the random velocities of dark matter particles were small could the small irregularities grow in size fast enough to trap baryonic gas and make it form galaxies. The matter had, therefore, to be cold, and we call this model of galaxy formation the cold dark matter model. The standard cosmological model is calledCDM: cold dark matter with a cosmological constant.

The parameters of our cosmology – the cosmological constant, matter fraction, and so on – leave their imprint on these fluctuations. The fluctuations occur on all length-scales, but they do not have the same size on different scales. The angular spectrum of fluctuations contains a rich amount of information about the cosmological parameters, and it is here that we find the constraints shown in Fig. 12.4.

Dark matter and galaxy formation: the universe after decoupling

Going forward from the time of decoupling, physicists have simulated the evolution of galaxies and clusters of galaxies from the initial perturbations. The density perturbations in the dark matter grow slowly, as they have been doing since before decoupling. But before decoupling, the baryonic matter could not respond very much to them, because it remained in equilibrium with the photons. Once the baryonic matter took the form of neutral atoms, it could begin to fall into the gravitational wells created by the dark matter.

Unlike the dark matter, the baryonic matter had the ability to concentrate itself at the bottoms of these wells, so that the density irregularities of the baryonic matter soon became stronger than those of the dark matter. The reason for this is that the baryonic matter was charged: as the atoms fell into the potential wells, they collided with one another and collisionally excited their electrons into higher energy levels. The density was low enough that the electrons then decayed back to the ground state by radiating away the excess energy. Now that decoupling had happened, this was a one-way street, a way of extracting energy from the baryonic gas and allowing it to clump inside the dark-matter wells. Astronomers call this process cooling, even though the net effect of radiating energy away is to make the baryonic matter hotter as it falls deeper into the potential wells!

The dark matter itself is not charged, so it cannot form such strong contrast. It forms extended ‘halos’ around galaxies today, as we shall see below. Extensive numerical simulations using supercomputers show that the clumps of baryonic gas eventually began to condense into basic building-block clumps of a million solar masses or so, and then these began to merge together to form galaxies. So although images of the universe seem to show a lot of well-separated galaxies, the fact is that most of the objects we see were formed from many hundreds or more of mergers. Mergers are still going on: astronomers have discovered a fragment of several million solar masses that is currently being integrated into our own Milky Way galaxy, on the other side of the center from our location. The unusual star cluster Omega Centauri seems to be the core of such a mini-galaxy that was absorbed by the Milky Way long ago. As mentioned in § 11.4, astronomers have found a massive black hole in its center. And the Magellanic Clouds, easily visible in the sky in the southern hemisphere, may be on their way to merging into the Milky Way.

In 2012 the European Space Agency plans to launch the astrometry satellite GAIA, which will measure the positions and proper motions of a billion stars to unprecedented accuracy. One of the many goals of GAIA will be to map the velocity field of the Milky Way, because astronomers expect that ancient mergers will still be apparent as ‘streams’ of stars moving differently from others.

Sometime during this hierarchy of merging structures, the density of the gas got high enough for the first generation of stars to form. These are called Population III stars, and they were unlike anything we see today. Since the gas from which they formed was composed only of hydrogen and helium, with none of the heavier elements that were made by this generation of stars and incorporated into the next, these stars were much more massive. With masses between 100 and 1000 M , they became very hot, evolved quickly, generated heavier elements, blew much of their outer layers and much of the new elements away with strong stellar winds, and then very likely left behind a large population of black holes. The ultraviolet light emitted by these stars seems to have re-ionized much of the hydrogen in the universe, which had been neutral since decoupling. All of this happened between redshifts of 10 and 20, the epoch of re-ionization. This was the epoch of first light for galaxies, the first time that the expanding universe would have looked optically a bit like it does today, if there had been anyone there to observe it!

After re-ionization and the generation of heavier elements by the first stars, the continued expansion of the universe led galaxies to be more and more isolated from each other, and they became nurseries for one generation of new stars after another, each with a bit more of the heavier elements. Our Sun, whose age is about 5 billion years, was formed at a redshift between 0.3 and 0.4.

One of the puzzles in this scenario of hierarchical structure formation is the appearance of massive black holes in the centers of apparently all galaxies. Astrophysicists do not yet know whether these formed directly by the collapse of huge gas clouds as the baryonic matter was accumulating in the potential wells, or if they arose later by the growth and merger of intermediate-mass black holes left behind by Population III stars. The fact that galaxy evolution is dominated by mergers suggests that the LISA gravitational wave observatory (see the previous chapter) will have an abundance of black-hole mergers to study.

Although physicists do not know what kinds of particles (or indeed, more massive structures like black holes) might make up the dark matter, and although the dark matter emits no electromagnetic radiation, it is possible to make indirect observations of it. One way it shows itself is in the rotation curves of spiral galaxies: in the outer regions of spirals the orbital speeds of gas and stars are much greater than could be accounted for by the gravitational pull of the visible stars. Indeed, observations suggest that in most spiral galaxies the total mass of the galaxy inside a given radius continues to increase linearly with radius even well outside the visible limits of the galaxy. This is the footprint of the dark matter density concentration within which the galaxy formed. The other way of getting indirect evidence for dark matter is through gravitational lensing. Astronomers have many images like Fig. 11.8, as we discussed in the previous chapter. Both of these methods involve essentially using gravity to ‘weigh’ the dark matter.