Thee CMBR

David Layzer is the Donald H. Menzel Professor of Astrophysics Emeritus at Harvard University. He is the author of two books, Constructing the Universe and Cosmogenesis, and was an associate editor of the Annual Reviews of Astronomy and Astrophysics for 30 years.

Cosmology became a science in the 1920s. During that decade Hubble's observational program with the 60- and 100-inch telescopes on Mt. Wilson supplied compelling evidence for the hypothesis that guided his program and was its central finding: that the observable universe is a fair sample of the universe as a whole. Friedmann's (1922) theory of a uniform, unbounded fluid, based on Einstein's theory of gravitation in its original form, predicted that such a fluid cannot be static but must expand from an initial singular state in the finite past. And to round off the decade, measurements of the redshifts of faint distant galaxies by Hubble and Humason showed that the system of galaxies was in fact expanding in the way predicted by Fried-mann's theory. The next major advance in observational cosmology was the discovery of the CMBR by Penzias and Wilson (1965a).

Not everyone was surprised. George Gamow had suggested that heavy atomic nuclei were formed by successive neutron captures in an early hot universe. Using measured neutron-capture cross sections he and his colleagues deduced the temperatures that would have had to prevail when the expanding universe was dense enough for successive neutron captures to produce (approximately) the observed relative abundances of heavy nuclei. On this basis they predicted that the radiation field, eventually decoupling from the matter, would retain its thermal character and would now have a temperature of about 10K. (Of course, as we now know, this prediction rested on a false premise. The heavy nuclei were formed in the cores of massive stars, not in a hot, dense cosmic medium.)

Others were surprised. The steady state cosmology, put forward by Hermann Bondi and Thomas Gold (1948) to explain a discrepancy between the estimated age of the universe (based on measurements of Hubble's constant) and the estimated age of the Earth, was still popular, especially among British cosmologists. In Sweden, Bertil Laurent and Oskar Klein had suggested that the universe is finite and bounded, an expanding island floating in empty space. These cosmological models became instant casualties of Pen-zias and Wilson's discovery. A thermal radiation field with a temperature of 3 K couldn't be formed in either of them.

Proponents of an initially cold Friedmann universe were also surprised. Lifshitz's (1946) theory of the growth of density fluctuations in a Friedmann universe had shown that thermal fluctuations in a uniform gaseous medium were many orders of magnitude too small to evolve into self-gravitating systems. To overcome this difficulty Zel'dovich (1962) suggested that an initially cold cosmic medium would solidify when its density reached approximately one tenth the density of water. Then, as it continued to expand, it would break up into solid chunks large enough to cohere under their internal gravitational attraction.

The path that led me to Zel'dovich's hypothesis was different. In 1951 I was a postdoctoral fellow in Ann Arbor, working on problems in atomic physics, when I came across a copy of Otto Struve's (1950) book Stellar Evolution. I was especially intrigued by Struve's account of binary stars and theories of their origin. Though half the stars in our neighborhood belong to binary or triple systems, neither of the two main hypotheses for the formation of binaries - the fission hypothesis and the capture hypothesis -could account for this fact. It occurred to me that if stars had formed in close proximity to one another - if the cosmic medium had once been a uniform distribution of strongly interacting protostars - then, as the medium continued to expand, most of the protostars would have ended up in small groups, the most stable of which would be binaries.

This thought immediately suggested to me that all self-gravitating systems might have been formed in this way, as clusters of smaller systems. The earliest stage in this process of hierarchical gravitational clustering would have been the formation of the smallest objects held together by their own gravity rather than by chemical cohesion. Clusters of these objects would evolve into planetary systems, clusters of these evolving systems would come together in larger self-gravitating clusters, and so on, up to galaxies, clusters of galaxies, and clusters of galaxy clusters. I wrote a short paper (Layzer 1954) in which I argued on the basis of this picture that the Solar System could have evolved from a cluster of marginally self-gravitating chunks of matter. I argued that this picture could explain why satellite systems like those of Jupiter and Saturn mimic the Solar System.

But it was just a picture, not a theory. Atomic physics was still the focus of my research. I hadn't studied general relativity nor read Lifshitz's (1946) seminal paper. I knew that the universe was expanding, and I assumed (correctly but for no good reason, then) that self-gravitating systems were not expanding with it. And that was the extent of my knowledge. So I began to study general relativity, with a view to acquiring more insight into the interplay between the disruptive tendency of the cosmic expansion and the tendency of overdense regions to contract.

Zel'dovich, in his 1962 paper, had used a theory of the growth of cracks in a stressed solid to estimate the sizes of the primordial fragments. His aim was to show that random (square root of N) fluctuations in a uniform distribution of these fragments would be large enough to evolve into self-gravitating systems. My approach centered on energetic considerations. Its aim was to understand not just how an initially uniform cosmic medium could ever become unstable against the growth of density fluctuations but to understand how it could become and remain unstable against the growth of density fluctuations on progressively larger scales. I reasoned that because the gravitational interaction has no inherent scale, gravitational clustering would have to be a self-similar process. Thus a log-log plot of (primordial) binding energy per unit mass against cluster mass would have to be a straight line, extending from the smallest self-gravitating systems to clusters of galaxy clusters. Observational evidence supported this conclusion; and the predicted slope of the relationship (based on a theory developed in Layzer 1968 and 1975, my 1968 Brandeis lectures in Layzer 1971, and my book Cosmogenesis, Layzer 1990) agreed with the observed slope. Moreover, the theory predicted a coincidence first pointed out, I believe, by Fred Hoyle (1953): the gravitational binding energy per unit mass of our own planetary system (and, presumably, others as well) is approximately equal to the chemical cohesion energy per unit mass of a typical solid (and of solid hydrogen).

By 1965 most of this work had been done, though not all of it had been published. So I greeted Penzias and Wilson's announcement with mixed feelings. Like most people who had opinions on such matters, I found the experimental findings and their interpretation convincing. Also like most people, I recognized that they would have momentous consequences for cosmology. At the same time, I felt pretty confident that the picture of hierarchical gravitational clustering was essentially correct. So I had to face the question: Can the existence of a thermal radiation background with a temperature of 3 K be reconciled with the picture of gravitational clustering in a cold universe?

If, as most people assumed, the background radiation was the remnant of a primordial fireball, its almost precisely thermal character would be easy to understand. On the other hand, if it was created by the burning of hydrogen into helium later in the history of the universe, two conditions would have to be met. The universe had to have been opaque to the background radiation (at the temperature it had then). And the mass density of hydrogen converted into radiation had to be less than the closure density. These conditions work in opposite directions. The farther we go back in time, the easier it is to construct conditions under which the universe will be opaque to radiation at the appropriate temperature. But because the energy per unit mass of the radiation field diminishes like the reciprocal of the cosmic scale factor, the second condition puts a lower limit on the epoch at which the radiation could have been created. Could both conditions be met?

A quick and dirty calculation suggested that they might be - though it would be a tight squeeze. So there seemed to be no reason to abandon the scenario of gravitational clustering in a cold universe - at least not yet. But to survive, the scenario needed to pass more stringent tests.

In the cold universe, as in standard hot models, helium is formed during an early era of nucleogenesis. Following a preprint by Jim Peebles, Michele Kaufman (1970) studied under what conditions this could be done in an initially cold universe. Her results were promising, but left unanswered a key question: Would helium created in an early cold universe be subsequently transformed into still heavier elements? Subsequently, Anthony Aguirre (1999) devised reasonable cosmological models that are cold enough to solidify at the appropriate time but warm enough to prevent helium from being consumed in the production of heavier nuclei.

Can the background radiation be adequately thermalized in an initially cold universe? The most recent calculations, again by Aguirre (2000), indicate that the answer is yes.

An attractive feature of the cold universe scenario is that it requires a large fraction of the (ordinary) matter in the universe to be nonluminous. For in the cold universe, the background radiation is produced by an early generation of massive (and supermassive) stars, whose ejecta supply both the dust that thermalizes the radiation and the nonluminous matter that makes itself known through its gravitational effects. This is attractive because it makes the existence of dark matter/missing mass a necessary feature of the universe, required by the production of the background radiation. And it makes two testable predictions. It predicts that the dark matter is ordinary matter and it predicts a small range of possible values for the ratio between dark matter and bright matter.

Recent observations of the microwave background and of the redshifts of distant galaxies seem hard to reconcile with the cold universe scenario. On the other hand, the standard hot scenario still lacks a compelling account of the origin of self-gravitating systems in the expanding universe. Whatever our views on the issue of hot versus cold - unlike most of my colleagues I remain an agnostic - we can all agree that Penzias and Wilson's discovery has changed not just the face but the character of theoretical and observational cosmology.

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