"Energies have been converted to their equivalent masses.

bThis includes enough electrons to make matter electrically neutral.

Source: Adapted from Fukugita and Peebles (2004).

"Energies have been converted to their equivalent masses.

bThis includes enough electrons to make matter electrically neutral.

Source: Adapted from Fukugita and Peebles (2004).

attraction produced by the mass equivalent of its energy. Near the end of the life of a massive star the pressure grows large, and that contributes to the final violent relativistic collapse of its central parts to a black hole. But pressure can be negative: the tension in a stretched rubber band is in effect a negative pressure. This negative pressure slightly reduces the gravitational attraction produced by the mass associated with the energy of the rubber. Einstein's A acts like a fluid that has nearly constant energy density, and pressure that is negative. In this case the negative pressure is large enough in magnitude that its gravitational effect overwhelms the gravitational attraction of the energy (as opposed to the exceedingly small effect of the tension of a rubber band). The result is a contribution to the gravitational field that pushes matter apart.9 The name "dark energy" comes from the intuition felt by many that A has something to do with an actual energy density, and that, like other forms of energy, A need not be exactly constant. But all we can say with confidence is that this term is needed to make sense of the evidence whose collection and analysis is the subject of Chapter 5.

9 It is best left as an exercise for the student to see why this push has little or no effect on how the dark energy itself is distributed, and why the negative pressure allows the energy density in this component to remain nearly constant as the universe expands.

The second component in the table is dark matter. It acts like a gas of particles that move freely, apart from the effect of gravity. Fritz Zwicky (1933) seems to have been the first to notice the dark matter effect. As discussed in a little more detail in the next chapter (in footnote 13 on page 31), he found that the observed mass in stars in the Coma Cluster of galaxies (named for the constellation in which it appears in the sky) is much too small to gravitationally confine the motions of the galaxies deduced from the Doppler shifts of the galaxy spectra. It seemed unlikely that the cluster could be flying apart, because the distribution of galaxies near the center of the cluster is smooth and quite compact. But what might be holding the cluster together?

Zwicky's effect has since been found to apply to the other rich clusters: the cluster galaxies are moving too rapidly, and the plasma in the cluster is too hot, to be held by the gravity of the mass present in the galaxies. The same applies to the motions of stars and gas in the outer parts of individual galaxies outside clusters. The mass that is needed to hold clusters together, and to do the same for the outer parts of individual galaxies, used to be known as "missing mass." It is now termed "dark matter," but we still do not know what it is, apart from one clue. The evidence we will be describing is that the dark matter cannot be baryons, for that would contradict the successful theories for the origin of the light elements and of the properties of the CMBR. The evidence instead is that the dark matter is a gas of freely moving nonbaryonic particles. Discovering the nature of these mystery particles, and the nature of the dark energy - Einstein's A - is a wonderful opportunity for search and discovery by the generations after us.

The second category in the table is the thermal electromagnetic radiation and neutrinos left from the hot big bang. The radiation - the CMBR - has the spectrum shown in Figure 2.2. This radiation now contains about 400 thermal photons per cubic centimeter. The mass equivalent to the mean energy of one of these photons is so small that the radiation mass density adds only a trace to the total. But you will recall that the cosmological redshift (shown in equation 2.2) reduces the photon energy as the universe expands. In the early universe the thermal photons were energetic enough that their mass densities were the largest contribution to the total. (This is discussed in more detail in footnote 9 on page 29.)

The energetic photons in the early universe took part in the creation and annihilation of neutrinos by the reactions to be discussed in the next chapter. That would have produced a thermal sea of neutrinos. The number of neutrinos plus antineutrinos in each of the three families is now 3/11 times the number of thermal photons, or about 100 neutrinos per cubic centimeter at the present epoch. The present energy density is larger in these fossil neutrinos than in the radiation however, because the neutrinos have rest masses. (The experimental evidence that neutrinos have masses is clear, but the values of the masses are only loosely bounded. The number in the table for the present neutrino mass density is an order-of-magnitude estimate. But we can be sure there is not enough mass in the known families of neutrinos to serve as the dark matter: we need another kind of mystery particle.)

The third category is the baryons. The total mass density in this form is inferred from arguments that again are discussed through this book. The inference (but at the time of writing not a demonstration by detection) is that most of the baryons are in the form of diffuse plasma, the first entry in this category, because this amount of baryons in any other physically reasonable state would have been observed. There is a trace amount of this plasma in the disks of spiral galaxies such as the Milky Way. There is a larger amount in hotter plasma in clusters of galaxies, and a still larger amount in plasma gravitationally bound to the outer regions of individual galaxies. There also is a sea of diffuse plasma spread through the enormous spaces between the galaxies. The relative amount in the last two forms is not well established.

The second component in the baryon category in Table 2.1 is the mass in stars that are radiating energy by nuclear burning - the nuclear reactions that convert hydrogen to helium and heavier elements - in their central regions. The stars in the nearly spherical bulges of spiral galaxies such as the Milky Way formed when the universe was much less than half its present age. Most of the stars in elliptical galaxies, which have at most an inconspicuous disk, also are old. The stars in the disk of the Milky Way have a broader range of ages. Stars are still forming at substantial rates in the disks of spiral galaxies and in lower mass galaxies such as the Magellanic Clouds, largely out of the neutral atoms and molecules entered as the fourth component in this category. But the overall rate of star formation is markedly lower now than it was when the universe was half its present age. There is a large mass of baryons in diffuse plasma, but this plasma is cooling too slowly to supply baryons for ongoing star formation at the past high rate.

As the energy supply in a star is exhausted some baryonic matter is ejected in stellar winds and explosions and some is left in stellar remnants: white dwarfs, neutron stars, and black holes. The third component in the baryon category is an estimate of what has accumulated in these remnants. There are baryons in many other fascinating forms, including planets and people, but they are thought to amount to a very small fraction of the total, as indicated in the last entry.

The fourth category is the accumulated energy released by stars in electromagnetic radiation - starlight - and neutrinos. The larger amount of energy in neutrinos is a result of the copious emission accompanying the collapse of dying massive stars. These energy densities are averages over large scales. We receive more than average starlight (after correction for the Sun) because we are in a galaxy of stars, the Milky Way. This local energy density in starlight happens to be comparable to what is in the CMBR, but the two have little else to do with each other.

The fifth category is an estimate of the energy density in gravitational radiation produced during the formation of black holes by the gravitational collapse of mass concentrations or by the merging of black holes. Several of the contributors to Chapter 4 mention their interest in detecting this gravitational radiation, but that is another story.

As we have said, the tasks of discovering the physical natures of dark energy and dark matter are at the time of writing golden opportunities for research for future generations. One of our tasks in the rest of this book is to consider the lines of reasoning and observation that have led to the conclusion that we do have credible evidence that these dark components really exist. We begin in the next chapter with an account of the early development of ideas that led to the identification of two very helpful fossils from the early universe: the thermal CMBR and the isotopes of hydrogen and helium.

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