Nucleosynthesis in alternative cosmologies

The evidence developing in the 1950s was that the heavier elements were produced in stars. If so, might the stars also produce light elements? If that were so, helium production in a hot big bang could be a problem: it might produce too much helium. But that was easy to fix: adjust the prediction by adjusting the assumptions in the big bang model, or go to an alternative cosmology, the steady state picture for example. We review here some of the alternatives people were considering. The point to notice is that in 1960 the relativistic hot big bang model for the universe was not the obviously best possibility: there were other ideas that were arguably as elegant. We needed observations to show the way through the thickets of elegance. Our purpose in this book is to trace the development of a large part of the evidence.

Let us consider first what came of the proposal that the heavy elements were formed in the big bang along with the light elements. A problem with this idea is that there is no stable atomic nucleus with mass 5 (that is, a total of five neutrons plus protons). That means the abundant isotope of helium, with mass 4, cannot capture a neutron and then another one and subsequently decay to an isotope of lithium by the emission of an electron. This strongly suppresses the build-up of elements heavier than helium during the rapid expansion of the early universe. Alpher (1948b) remarks on the problem, and a like situation at mass 8, in the published version of his doctoral dissertation. The analysis mentioned above by Fermi and Turke-vich failed to find a nuclear reaction that might carry significant nuclear burning in the early universe past the mass-5 gap. But Gamow (1949) noted a possible way out that is worth considering even though it proved to be wrong: false steps can be edifying.

Gamow's idea was that if the mass density in baryons when the temperature of the universe was Tcrit were much larger than previously considered, and n/p were smaller (as, it was later realized, follows from Hayashi's 1950

analysis of equation 3.9), then after all the neutrons had combined with protons to form heavier elements a substantial fraction of the baryons would be left as protons, the nuclei of hydrogen atoms. That agrees with what is observed: hydrogen is the most abundant element. The larger matter density in the early universe would cause faster nuclear burning of deuterium, and perhaps that could push nuclear burning past mass 5 to make the heavier elements. We see another consequence that attracted no attention then: when the matter density had dropped to the present value the radiation temperature would have been much lower than in the hot big bang Gamow had introduced earlier.

Hayashi and Nishida (1956) presented an analysis of this idea. They considered the possibility that the baryon number density at temperature T = 1010 K is at least a hundred million times what is assumed in Gamow (1948a) and Alpher and Herman (1948). That lowers the present temperature of the CMBR by a large factor, which Hayashi and Nishida would not have counted as a problem because the CMBR was not known. They took account of the helium-burning reactions

4He +4He ^8Be + y, 8Be+4He ^12C + y, 12C+4He ^16O + y, (3.11)

which by then were known to be important in the evolution of stars after all the hydrogen in the central regions had burned to helium. In this "cool" big bang model universe, Hayashi and Nishida found significant production of carbon and oxygen. The deuterium abundance coming out of this model is much too small, according to what is now known, and the helium abundance is too large, though not by a large factor.16

This cool big bang universe produces helium in an amount that might not have seemed unreasonable at the time. It also produces a not insignificant amount of heavy elements. Layzer and Hively (1973) pointed out that the heavy elements produced in such a cool big bang might form dust grains that were able to absorb and reradiate starlight effectively enough to have produced the thermal CMBR spectrum out of starlight. Here is an example of an idea that is interesting but was not pursued, and as it happened later proved to be not viable. The light element abundances are wrong, and the picture cannot account for the relation between the large-scale distributions of matter and the CMBR that is discussed in Chapter 5.

Zel'dovich (1962, 1963a,b, 1965) proposed lowering the temperature all the way, to a cold big bang in which element production is left entirely to the

16 That is because almost all the neutrons that survive to the time when the temperature has fallen to Tcrit are burned to helium, and the value of n/p when deuterium starts accumulating is not very sensitive to the density of matter.

stars. He was led to this picture by his impression that the helium abundance in some stars is quite small.17 His evaluation of the Gamow condition (in footnote 10 on page 30) led him to conclude that a hot big bang cosmology could only account for the low helium abundance if the present-day universe were hot, T0 ~ 30 K (at his estimate of the present baryon mass density, 10"29gcm-3; Zel'dovich 1963a), well above what was later observed. That is because a higher temperature today, at a given present mass density, implies a lower matter density at Tcrit, which means fewer nuclear reactions that produce less helium, as Zel'dovich thought was required.18 He argued that this high present temperature is unlikely because it would imply strong scattering of the thermal photons by fast-moving electrons, unacceptably limiting lifetimes of cosmic ray electrons.

Later developments on this issue are very relevant to our story. In a note added in proof in a paper published later that year Zel'dovich (1963b) stated that the latest data "indicate the temperature of intergalactic thermal radiation is below 1°—0.5° K," which would add to his arguments for a cold big bang. Zel'dovich (1965) later mentioned the likely source of these data, Ohm (1961). The origin of Ohm's landmark paper, which actually could be read to suggest the presence of a sea of microwave radiation, is outlined in Section 3.5 beginning on page 44; Hogg describes the situation in more detail in Chapter 4 (beginning on page 70). Novikov (p. 99) explains why he and Doroshkevich, who were members of Zel'dovich's research group, were particularly interested in Ohm's paper. Novikov and Smirnov describe Zel'dovich's reaction to news of the identification of the CMBR. His reaction is illustrated also in Zel'dovich's letter to Dicke quoted on page 196. But this happened later: in 1963 Zel'dovich saw a good case for a cold big bang. It is worthwhile considering how he found what seemed to be a viable theory.

In Zel'dovich's cold model the very early universe contained equal number densities of protons, electrons, and neutrinos, all very nearly uniformly distributed, and cold, meaning the particle energies are as low as possible. This means one has to consider the effect of the exclusion principle that

17 Zel'dovich (1963a) mentions evidence of stars with helium abundance Y as low as 2.5% by mass. He adds the careful statement (in the English translation) "We cannot make any estimate of the reliability of these results." But the paper proceeds on the assumption that Y is not more than about 0.1. Osterbrock (p. 86) describes the evidence known then that Y is larger than that.

18 Smirnov's account of Zel'dovich's suggestion that he reanalyze element production in a hot big bang, and perhaps increase the challenge for a hot case, commences on page 94. The results, in Smirnov (1964), showed that the small primeval helium abundance he thought he should be aiming for could be accommodated in the hot big bang picture by lowering the matter density at a given radiation temperature, as Zel'dovich had proposed, but that would imply an unacceptably large abundance of deuterium. This is because at the lower densities Smirnov considered neutrons and protons combine to form deuterium, but the burning of deuterium to helium is incomplete.

limits the allowed number densities of electrons and neutrinos at a given energy. The high density of electrons in this cold early universe would cause the electrons to occupy all their available states up to a large energy. The energetic electrons would normally force themselves onto protons to make neutrons, by the first reaction going to the right in equation (3.9). But that is not allowed here because it would require the production of neutrinos, and in this picture all the neutrino states with the energy allowed by the reaction are already taken.19 In this universe star formation would commence with nearly pure hydrogen. This is yet another interesting universe that proves not to be the one we live in.

Hoyle and Tayler (1964) knew that the helium abundance is large, and greater than seemed reasonable for production in stars. They too reconsidered the hot big bang model, but they also pointed to another possibility. In the steady state cosmological model the universe always has been as it is now: there would be no fossil helium. Hoyle and Tayler suggested that the helium could have been produced in the "little bangs" of very massive exploding stars. The evolution of temperature and density within a very hot exploding star is similar to the evolution in an expanding universe, so element formation is similar too. Worth noting here is that the energy released by the conversion of hydrogen to the observed amount of helium would produce radiation energy density comparable to what is in the CMBR.20 Here is an elegant unified theory of the origins of helium and the CMBR, but it is yet another universe that we know is not ours. Like cool and cold big bangs, it cannot account for the measured properties of the thermal CMBR discussed in Chapter 5.

Still another alternative, which could eliminate fossil helium while leaving us with the fossil CMBR thermal radiation, was the idea that the laws of physics might change as the universe expands. An example of particular interest then (and now) is that gravity, which is weak now, might have been stronger in the past, making the early universe expand too rapidly to allow

19 Another way to put this is that Zel'dovich assumed the lepton number mentioned in footnote 15 on page 32 is positive and large enough to force the equilibrium ratio of neutrons to protons at high density and low temperature to a value close to zero. Zel'dovich's idea of adjusting the cosmic lepton number can be extended to a hot big bang model; it changes the relation between the helium abundance coming out of the big bang and the CMBR temperature. The evidence now is that the lepton number is negligibly small (Steigman 2007).

20 Suppose, for example, that 25% of baryon matter density p = 10_29 gcm-3, a value often discussed then, were burned from hydrogen to helium, with the conversion about 0.005 times the mass in helium to radiation (depending on what fraction of the released nuclear binding energy is lost to neutrinos, redshift, and maybe remnant black holes). Using the relation between temperature and blackbody radiation energy density in footnote 9 on page 29, we see that this energy is equivalent to radiation temperature T = 6K. This line of thought is discussed further on page 58 and in the contributions by Faulkner (beginning on page 251) and Burbidge and Narlikar (beginning on page 267).

time for any appreciable build-up of the elements. This idea was inspired by the following consideration.

A measure of the relative strengths of the gravitational and electromagnetic interactions is the ratio of the gravitational and electric forces of attraction between an isolated electron and proton:

The charges of a proton and electron are +e and —e, their masses are mp and me, and G is Newton's gravitational constant. Since both forces vary in the same way with the separation of the particles, this ratio does not depend on the separation. Its small value - gravity is a very weak force compared to electricity - led Dirac (1938) to ask whether the strength of the gravitational interaction might be decreasing: maybe gravity is exceedingly weak now because the universe is very old. Alpher (1948a) mentioned the idea, and a consequence: if gravity were stronger in the past then the rate of expansion of the early universe would be larger than is predicted by general relativity theory (because stronger gravity then required a larger rate of expansion to escape the gravitational pull). That would affect the computations of element formation. Alpher quoted Teller's (1948) argument against the idea: if gravity were significantly stronger when Earth was young then the Sun would have been significantly hotter, making early life on Earth impossible. But beginning in the 1950s Pascual Jordan and Robert Dicke reconsidered Teller's argument and concluded that the observations might instead suggest that the strength of gravity is evolving. The important consequence of this line of thought for the purpose of our story is its effect on Dicke's thinking about the early universe.

Dicke felt that Dirac's proposal is an appealing illustration of another idea, which he, Dennis Sciama, and others termed Mach's principle.21 Following earlier discussions, Ernst Mach (1883) had asked what determines the motion of a body that is moving freely and without rotation. It seemed unlikely to Mach that this free or inertial motion is an intrinsic world feature; he supposed rather that inertial motion is determined by motion relative to all the rest of the matter in the universe.22 It seemed likely to Dicke that if

21 Sciama (1959) and Dicke (1964) review their thoughts on what Mach's principle might mean for cosmology. These ideas still attract attention, but have not been fixed within a definite theory. The term Mach's principle accordingly means different things to different authors.

22 Mach's arguments played an earlier role in the development of cosmology. Einstein considered them to be one of the guides to his general relativity theory: matter is the source term in the field equation that determines the geometry of spacetime, roughly what Mach and others had in mind. But the theory allows a universe in which there is an island of matter in a spacetime that is arbitrarily close to flat at arbitrarily great distance from the matter. A particle could escape inertial motion were determined by what all the rest of the matter around us is doing then the same may be true of other aspects of physics, including gravity. Perhaps the thinning of the mass distribution around us as the universe expands causes the strength of gravity to decrease.

Jordan's thoughts about Dirac's proposal led him to the idea of an adjustment of general relativity to a scalar-tensor gravity theory in which the number in equation (3.12) decreases as the universe expands. The first version of this new theory is in Jordan (1952). Jordan (1962) summarizes ideas about possible observational consequences, largely on Earth's evolution. Dicke's reading of Mach's principle led to the exploration of the scalar-tensor theory in Brans and Dicke (1961). Dicke was taken with the idea that, in this theory, gravity in the very early universe could have been so strong that the universe was expanding so rapidly23 that there was no production of elements heavier than hydrogen. That led to the comment in the letter from Dicke to Sciama quoted on page 199: at the time Dicke thought there is a good case for a hot big bang that left the fossil CMBR but no helium before nuclear burning in stars (Dicke 1968).

The Jordan-Brans-Dicke theory is another example of an idea that fascinates but fails, at least in its original intended application: we have tight experimental limits on any possible variation of the strength of the gravitational interaction or on many other conceivable departures from general relativity theory. Interesting ideas tend to be durable, however. This theory, and the idea that numbers such as the one in equation (3.12) may vary with time, continues to figure in debates about the physics of the very early universe.

In the 1950s and earlier it was logical to consider yet another departure from what had become conventional ideas: perhaps our universe of galaxies is not close to homogeneous. Perhaps the observed tendency of matter to this island of matter, move arbitrarily far away, and yet retain its usual inertial properties. If the particle were large enough to house an observer with a gyroscope, the observer could determine whether the particle is spinning by referring to the motion of the gyroscope. But spinning relative to what? Einstein (1922a,b) noted that this situation is possible within general relativity theory, but he argued that if the universe were constructed this way "then Mach was wholly wrong in his thought that inertia, as well as gravitation, depends upon a kind of mutual action between bodies" (Einstein 1922a, p. 109). The problem is avoided if, as Einstein (1917) had proposed, matter uniformly fills space — apart from local irregularities. This picture of a homogeneous universe came to be known as the "cosmological principle." There are isolated island universes of matter, the galaxies. But the cosmological principle has proved to be a good approximation to the observed large-scale mass distribution. We do not know whether Einstein arrived at the right picture for the large-scale structure of the universe for the right reason. 23 If this seems counterintuitive consider, as we have remarked earlier, that stronger gravity would more rapidly slow the rate of expansion, so the expansion rate would have had to have been larger to allow the universe to reach its present state. A more formal argument is in the first part of equation (G.1) increasing G when the mass density is large would make the expansion rate a/a larger than in standard physics.

be concentrated in galaxies, which are in turn found in groups and clusters of galaxies, extends in a hierarchy of clusters within clusters to the largest observable scales. Charlier's (1922) map of the distribution of the galaxies shows that this clustering hierarchy picture is a better fit to what was then known than Einstein's homogeneous universe. An alternative, in von Weizacker's (1938) discussion of how the elements may have formed, is that the universe of galaxies is bounded and expanding into empty asymptotically flat spacetime. Observers tended to like these pictures because the galaxies are distributed in a decidedly clumpy way. Thus a report by Oort (1958) on the observational situation commences with the sentence, "One of the most striking aspects of the universe is its inhomogeneity." We remarked in footnote 22 that Einstein disliked the idea, but other theorists found it attractive: Charlier (1922, 1925) and Klein (1958) presented well-reasoned arguments in favor of large-scale departures from a homogeneous mass distribution. These arguments are worth reading, but they are not much heard now because the other side won by the weight of the evidence.

Oort (1958) remarked on one of the pieces of evidence: the counts of progressively fainter galaxies increase about as expected in a homogeneous universe. (The relation is shown in equation 3.18 on page 55). By the early 1960s the distributions of radio sources and the X-ray background radiation were observed to be close to isotropic across the sky. Radio waves and X-rays seem to propagate through intergalactic space without significant scattering. That means they could only be seen to be isotropic if we were in a special place, close to the center of the expanding cloud, which seems unreasonable, or else if the universe were close to homogeneous.24 The network of evidence discussed in Chapter 5 shows that on the scale of the Hubble length mass density fluctuations amount only to a few parts in one hundred thousand. Einstein's picture of a reasonable universe, one that is close to homogeneous, was right.

These are examples of how elegant ideas may lead us astray or to aspects of reality. Let us consider next an arguably questionable idea that led to a decidedly interesting part of reality.

3.3 Thermal radiation from a bouncing universe

A big step toward sorting out all these ideas was the discovery of a fossil: the sea of microwave radiation that smoothly fills space. The chain of ideas and events that brought this radiation to the attention of the community includes the thought that our expanding universe might have bounced from

24 The argument is given in more detail in Peebles 1971, p. 40.

a previous collapse. As we will discuss, the bounce might be expected to have filled space with thermal radiation.

The notion of a bouncing or oscillating universe certainly was not ignored. Lemaitre (1933) had expressed the feeling that, from a purely aesthetic point of view, a universe that successively expands and contracts to exceedingly small size has "un charme poetique incontestable et faisaient penser au phenix de la legende." De Sitter (1933) was not so positive: "Personally I have, like Eddington, a strong dislike to a periodic universe, but that is a purely personal idiosyncrasy..." But he noted that a collapsing universe is unstable against the growth of departures from homogeneity, meaning different regions arrive at high density at different times. In a patch that does not become too dense most stars may avoid collisions; they may instead pass each other and move apart to join the new general expansion. Alpher, Bethe and Gamow (1948) suggested consideration of a bounce resulting from the net angular momentum of the universe. Wheeler (1958) put it that the bounce in an oscillating universe might be compared to "a glove which is turning itself inside out one finger at a time." Hoyle and Narlikar (1966) considered another variant: perhaps the universe is in a steady state overall, but "pockets of creation" set a part of the universe into a local oscillation. But the important notion for our purpose is Tol-man's (1934) remark that a bounce could produce entropy, largely in the form of a sea of thermal radiation. Weinberg (1962) found a related result: neutrino emission and absorption in an oscillating universe would drive the distributions of low energy - and massless - neutrinos and antineutrinos to the form characteristic of thermal equilibrium. And at roughly the same time Robert Dicke (in an unpublished discussion that is described more completely in the essays in Chapter 4) made Tolman's picture of the production of thermal electromagnetic radiation during a bounce more tangible, as follows.

Dicke noted that the nuclear burning of four protons - the nuclei of hydrogen atoms - to form the nucleus of one helium atom in a star releases enough energy to produce roughly a million starlight photons. The burning of helium to heavier elements produces still more starlight photons. These starlight photons are shifted toward the red as the universe expands. If the expansion eventually stopped and the universe collapsed back to high density then during the collapse the starlight photons would be shifted toward the blue, to greater energy. If the blueshift were large enough then just a few blueshifted starlight photons would have enough energy to break apart each heavy atom, reducing it to protons. These protons would serve as fuel for nuclear burning in new generations of stars in the next cycle of expansion and collapse. The rest of the starlight photons would be thermalized, that is, turned into what we observe as the CMBR.25 A few hundred bounces could make the observed energy density in thermal radiation out of starlight in a universe like ours, if the bounces conserved the numbers of baryons and photons.

Dicke had hopefully put aside, as a possibly minor nuisance, the developing evidence that general relativity is an incomplete theory of spacetime going forward in time to relativistic collapse to a black hole, and maybe incomplete also going backward in time to the big bang. Ellis (p. 379) recalls the gathering storms of the relativistic singularity theorems. The problem is still with us: general relativity cannot give a complete description of the arbitrarily remote past of our universe. But the general idea of a bouncing or quasiperiodic universe continued to attract interest (Steinhardt and Turok 2007). And it proved to be interesting enough in the 1960s that Dicke was able to persuade two members of his Gravity Research Group, Peter Roll and David Wilkinson, to build an instrument capable of detecting a sea of thermal microwave radiation.

News of the Roll-Wilkinson experiment reached Arno Penzias and Robert Wilson at the Bell Telephone Laboratories in Holmdel, near Princeton University. Hogg (p. 70) and Penzias and Wilson (pp. 144-176) recall the communications experiments that led to the detection of more microwave radiation than could be accounted for from known sources in and around their instruments. The essays in Chapter 4 recall how the news came to the attention of astronomers who saw that the radiation could account for the curious behavior of cyanogen molecules in the gas between the stars. The astronomers' puzzle and its resolution is our next topic.

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