Science
Hong Yee Chiu’s review of the state of cosmology in 1968
Abstract
Professor Hong-Yee Chiu, worked at NASA’s Institute for Space Studies from 1962. Born in Shanghai, he was educated at the Universities of Taiwan, Oklahoma State and Cornell. He taught at Columbia and Yale Universities, worked at the Institute for Advanced Study in Princeton for two years and wrote many papers on different fields of astrophysics.
Contents Updated: Wednesday, April 19, 2000
Check the next paper to see the progress over the next thirty years.
Cosmology, like all sciences, must be based on observational or experimental data, but until the post war period of the last twentieth century, relevant data were virtually non-existent, and cosmology became the hunting ground of speculators. Some based their theories on hypothetical assumptions concerning small violations of physical laws, others based them on cosmological principles imposed by man. Interesting as these theories were, they have contributed little to an understanding of the evolution of the universe.
Cosmology is a branch Of physics and subject to the laws of physics. Speculations should be verifiable in the laboratory of physics. Because we are dealing with cosmological scales (of a time duration of the order of 10,000 milion years or of a spatial extent of 1028 cm) one may argue that laws verified in the laboratory may not be applicable to the universe, and that one must invent different laws. This approach is incorrect. Evidence shows that many well established physical laws are applicable to the universe.
Th the course of a human life span (say 70 years or 2 x 109 seconds) the rotation of the galaxy enables astronomers to sample a volume of space measuring 1017 x 1014 x 1014 cm. Suppose a physical constant (such as the electron charge or the gravitational constant) were position dependent or time dependent and changed with respect to other physical constants during the universe’s evolation. If its magnitude altered by a factor of two in the life span of the universe (about lO18 seconds) or over the dimension of the universe (about 1028 cm) an experinent performed to an accuracy of one part in 1010 would detect the change over the span of a human life time.
Experiments of even greater accuracy have heen performed. Vernon W Hughes of Yale University has shown that any difference between the charge of electrons and the charge ofthe nucleus has to be less than one part in 1021. In other words, atoms can be taken to be strictly neutral. Hughes has also shown that the electron charge stays constant to one part in 1017 for electrons with velocities up to 0.l that of light and that mass is strictly isotropic to an accuracy of one part in 1022. Frederick Reines has discovered that if protons were unstable, their lifetime must exceed 1026years—much longer than the age of the universe. Robert H Dicke and his associates at Princeton University have shown that the gravitational constant is constant (as measured against the elertroiagnetic interaction) to one part in l09 over a prriod of one year. If Dicke can extend his measurement by two or more powers of ten, then the crucial question as to whether the gravitational constant is constant with time can be answered.
If all Cosmological theories which contain specclations violating accepted physical laws are excluded, then only one type can be considered. This is the oosmology originally formulated in 1922 by Albert Friedmann, a Russian physicist, and which was based on Einstein’s theory of general relativity.
Why is Einstein’s theory favoured over others? Because it is based on one very important property of gravitation: the trajectories of partic1es in a gravitational field with the same initial velocities and positions are identical and do not depend on the nature of the particles. This is certainly not true for the electromagnetic field—an electron will be repelled by the field of another electron while a positron will be attracted by it. This property enabled Einstein to treat the gravitational field as a geometrical property of space-time. Hence the theory of gravitation can be formulated by using geometrical theory, the one used being Riemannian geometry.
Einstein’s theory contains no additional constants. The gravitational constant in Einstein’s theory is the same as that used in Newtonian theory. In other theories additional constants appear. Einstein’s theory also agrees well with the three or four tests of general relativity that have been carried out. It has been argued that these tests do not exclude other theories because of experimental inaccuracies. A theory has a right to exist only after it is verified by experiments. Einstein’s theory has been verified by observations, even though the verification is not very accurate. But other theories have not been verified to any degree of accuracy. A theory should not be used simply because it fuiflls a philosophical need. For this reason, Einstein’s theory is favoured over the others.
For a theory as complicated as Einstein’s (it contains ten equations plus a number of subsidiary conditions). one might expect a large choice of cosmological theories. Surprisingly, Einstein’s theory provides only one type of cosmology, that of an evolving universe, assuming only that the matter in it is uniformly distributed—that it is isotropic and homogeneous. This was the cosmology first worked out by Friedmann.
The Einstein-Friedmann theory predicts a universe in constant motion which originated with a zero radius—a singularity—and subsequently. This is essentially the Big Bang theory. But the expansion could be permanent, in which case the universe is said to possess a negative curvature or to be an open universe. Alternatively, the expansion could slow down and be replaced by a contraction at some later time. Thereafter the universe would contract until its radius equalled zero. This type of universe is said to possess a positive curvature or to be a closed universe.
Certainly nothing can possess a zero radius in the real world. A zero radius would mean an infinite density—a premise not acceptable to most physicists. On the other hand, the general relativity theory is a classical theory—it is not applicable to atomic or sub-atomic phenomena. At present, no successful quantum theory of gravitation has been developed—and no solution is in sight. Hence we do not know how the universe would behave when its radius was almost infinjtely small.
Whether a universe is open or closed is determined by its density of matter and the energy within it. According to present data the universe is closed if its density exceeds 3 x 10-29 g/cm3, otherwise it is open. The present density of matter in galaxies is 7 x l0-31 g/cm3. Does this mean that the universe is open? Not necessarily because matter and energy can exist in forms other than galaxies.
One final word about the characteristics of open and closed models. In a closed universe the total amount of matter and energy is finite. The universe expands from a zero radius and then starts to contract after reaching a maximum radius, eventually returning to zero radius. What happens afterwards is not known, or at least is not clear from Einstein’s theory. The closed model is sometimes called an oscillatory model because some relativists believe that a closed model can be continued by adding another closed model after a zero radius has been reached. The universe then will undergo expansion and contraction again and again. But as far as is known, within the framework of Einstein’s theory of gravitation, expansion and contraction will occur only once. It can be argued that since Einstein’s theory is not valid at the origin of the universe, an unknown mechanism may cause the universe to reverse its direction of motion when it contracts to a critical radius. However, no known mechanism can achieve oscillation and it is premature to speculate some possible mechanism.
In contrast, an open universe expands forever. When the last star has consumed all its nuclear energy, the universe will be in total darkness. It will be dead, but still expanding. There are certain theoretical difficulties associated with this model.
The main difficulty lies in the fact that the total energy of such a universe is not defined. When all the energy is added up, one gets an absurd result: the energy is infinite. However, this difficulty originates from the fact that the universe has an infinite volume. Why should the universe estend to infinity? It appears more natural that it should end somewhere, but, so far, this diiiculty—though fundamental—has not been resolved.
The Einstein-Friedmann Universe, after about 1O-6 second, reaches a density of the order of 1014 g/cm3, which is the same as that of an atomic nucleus. The temperature at this stage is about 1013 °K. Under these conditions, the composition of matter is complicated. Even protons are not stable and undergo reactions which convert them into other fundamental particles. Antiprotons and antineutrons are created and the energy density of neutrinos is high.
As the universe expands, matter and radiation cool down. When the temperature drops to 1010 °K virtually all strange particles and antiparticles (except positrons) have disappeared. Remaining are protons, electrons, positrons, neutrons and neutrinos.
Because of the nature of particle-anti particle interactions, it is not possible for particles in thermodynamic equilibrium to separate from antipartides. Einstein’s theory of gravitation, the existence of particle-antiparticle interaction and the recognized laws of physics prohibit the co-existence of particles and antiparticles in the universe. In other words, Einstein- Friedmann cosmology excludes the existence of galaxies composed of antimatter.
When the temperature drops to 109 °K, a large fraction of electrons and all positrons are annihilated, enriching the energy of radiation. The composition of matter at this temperature is protons, neutrons, electrons, radiation and neutrinos. The latter, which also include antineutrinos, play a negligible role in the further course of evolution.
Between a temperature of 109 °K to a few times l08 °K, a build-up of elements from protons and neutrons takes place. At higher temperatures, nuclei are unstable and they will break up as soon as they are formed. At lower temperatures, the nuclear reactions are too slow against the expansion time of the unverse. The temperature range Of 100 °K to a few times l08 °K is just right for the build-up of elements. The time the universe spends in this temperature range is about 1000 seconds. Duriug this time protons and neutrons form deuterium, which combines with another proton to form helium-3, and that in turn reacts with another neutron to give helium-4. By the end of the universe’s first half hour 20 to 30 per cent Of the protons have been converted into helium.
When the temperature falls below a few times 103 °K, electrons and ions will have almost completely recombined, leaving only a trace amount of matter (l0-3 to l0-4 of all matter) frozen in the ionized state. As long as the radiation energy density exceeds the matter energy density, gravitational condensation of gas masses into galaxies and stars cannot take place. This is because radiation is a “light gas”. Its pressure is far too great for the gravitational attraction it generates to hold it together. But because of the way the energy density decreases with expansion of the universe, radiation energy density eventually becomes less than matter energy density. This happens at about room temperature—300 °K.
The condition for gravitational condensation at a given temperature and density involves a certain scale lengh. Gravitational condensation will take place if the dimension involved exceeds this scale length. The scale length involved at a temperature of 300 °K is about l021 cm, and a volume of the universe with that diameter would contain a mass of the order of 1039 grms. These values are too small to account for the mass of most galaxies but they imply that objects of a mass smaller than lO5 solar masses cannot be condensed in the intergalactic medium. The smallest galaxy observed has a mass close to 105 solar masses However, Dicke and P J Peebles at Princeton have suggested that globular clusters which also have a mass of lO5 solar masses are formed at this stage, before galaxies.
Once galaxies or globular clusters exist, stars are formed. The observed mass of stars range from 0.1 solar naass to 60 solar masses. The nuclear energy content of a star is roughly a few tenths of a per cent of its rest energy, and the luminosity of a star is roughly proportional to the third power of its mass. Thus the life span of a 60 solar mass star is of the order of one million years, but that of a star of 0.8 solar mass is nearly 20,000 million years. Since the projeeted age of the universe is 10,000 million years, some of these oldest stars may contain the primordial matter that was manufactured in the first half hour of the universe. Such stars should contain nearly 20 per cent helium but none of the heavier elements such as iron and carbon.
It is known that heavy elements are formed in the stars. When stars become supernovae and explode, these elements are elected into space. Interstellar gas thus becomes enriched with heavy elements, implying that younger stars should have a higher heavy element content than older stars. Indeed, stars can be caassified into two populations: population I stars, in the spiral arm of a gataxy, and population II stars in the nucleus and the large halo region of a galaxy. The heavy element content of population I stars is about three per cent but for population II stars it is much less than one per cent—and in certain populations no spectral lines from heavy elements have ever been observed.
There are two ways of testing the Einstein-Friedmann cosmological model. The first concerns the geometrical structure of space-time. In other words, one tries to observe the curvature of the universe. In the second test, one tries to observe the physical phenomena associated with the universe.
The sign of the curvature of the universe—the openness or closedness of a particular model—is determined by the rate at which the expansion is slowing down. This rate is characterized in astronomy by a parameter called q0. For a universe consisting mainly of matter (like our own), the sign of the curvature is positive (closed universe) if the value of q0 exceeds 0.5. The sign of the curvature is negative (open universe) if it is less than 0.5. In all cases, the value of q0 is proportional to the density of matter in the universe as it is the latter which, through gravitational attraction, slows the expansion. The parameter q0 is directly related to the speed of recession of very distant astronomical objects compared to much nearer ones. The linear relationship between distance and recession speed is now known to break down at velocities near that of light. But the way it breaks down should reveal which cosmological model is correct. Allan R Sandage has used this property to study the curvature of the universe. His recent result shows that the value of q0 is very close to unity but the error is still large—of the order of 50 per cent. If this result is taken literally, then the umverse is a closed one. But a word of caution is needed. The work is still being carried out by Sandage and his collaborator, J Kristian. They are optimistic about their ability to obtain a more accurate value of the deceleration parameter.
The other direct source of cosmological information is the primordial radiation, once hotter than all the nuclear fires combined, which has now cooled to 3 °K. At least a part of this has already been detected.
In the early 1960s Drs A A Penzias and R W Wilson at Bell Telephone Laboratories undertook an experimental programme to measure the microwave noise at 7 cm wave-length due to the atmosphere. The apparatus consisted of an aerial pointing towards an arbitrary direction in the sky. Slowly the aerial was directed towards zenith. One should expect that the noise due to the atmosphere should decrease towards zenith. Indeed this was observed, but when they extrapolated their results to zero zenith height, Penzias and Wilson found a small amount of residual radiation corresponding to a black body radiation of 3 °K at this wavelength. When they communicated their findings to Dicke, he was not in the least surprised. He had constructed a similar apparatus but with the specific intent of searching for remnants of the primordial radiation. What Dicke, Penzias and Wilson did not realize was that Gamow and his associates had already predicted the existence of a black body radiation of a few degrees above the absolute zero some 14 years earlier but their paper had been forgotten.
According to a recent calculation I have carried out with David Framm, a senior student from Princeton, the deviation of the cosmic radiation from the black body radiation should be exceedingly small—around one part in 106. To date, about seven points have been measured, all in good agreement with a cosmic black body radiation at a temperature of 2.7 °K, confirming what one would expect on theoretical grounds from the Einstein-Friedmann cosmology. Further, if this radiation is really cosmic in nature, it should be strictly isotropic. Its isotropy has been recently confirmed to an accuracy of 0.1 per cent.
Aocording to cosmological theory, the helium content of matter from one hour after creation until star formation should be between 20-30 per cent. If helium lines can be found in the oldest stars then we will be able to demonstrate that the temperature of the universe was once as high as 109 °K.
The type of stars for which we are looking, are population II stars, which are old stars. However, their surface temperatures are quite low (in the neighbourhood of 3000 °K or less). Helium lines can be excited only in the hottest stars (with a surface temperature of 104 °K or greater). Hence in ordinary population II stars the presence of helium cannot be detected. Helium lines have been detected in some population II stars which have evolved away from the main sequence and have a higher temperature but the exact helium content is not known.
These two tests are the most important currently being carried out in a number of laboratories and observatories. But there are at least three other possible tests. First, the Einstein-Friedmann cosmology predicts no antiparticles in the universe. Thus far no antipartides have been detected in cosmic rays. However, the experimental upper limit for antiproton flux is far from satisfactory for this kind of work. Second, agaln according to the Einstein-Friedrnann cosmology, there should be at most only a small amount of ionized gas in intergalactic space. No experimental upper limit or lower limit is yet available. And, third, the neutrino and antineutrinos should also have a black body spectrum with a slightly lower temperature (about 2.2 °K). However, the detection of such neutrinos is, as far as we know, beyond even the realm of theoretical possibility.
Despite the success of Einstein-Friedmann cosmology, there are still some serious difficulties. The most prominent is the inconsistency between the age of the oldest stars in our galaxy and the age of the universe. The theory of stellar evolution tells us that after a certain fraction of stellar nuclear energy is consumed, stars evolve away from the main sequence to the red giant region (characterized by high luminosity and low surface temperature). The time when they do this is strongly dependent on their mass but practically independent of their chemical composition. According to Sandage the age of the star cluster NGC 188 is 1.5 (+ or - 0.2) x 1010 years. Embarrassingly, we do know that the universe is no older than 1.3 x 1010 years. Indeed, if the value of q0 really is unity, then the actual age of the universe is only 8000-9000 million years—much too small to account for the existence of the old star clusters. A barely acceptable premise is to admit that the energy density of the universe is the erergy density of galaxies, namely 7 x l0-31 g/cm3. This will give a very small valve of q0 and an age for the univesse of very nearly 1.3 x 1010 years. But there is a contradiction here and one which can be resolved only by further study of those very distant astronomical objects which hold the answers as to exactly how the universe began and evolved.
Although we still do not know which cosmological model applies exactly to the universe, we have made tremendous strides in the right direction. Cosmology has finally emerged as a laboratory science and not merely as an exercise in speculation, the main purpose of which was to satisfy the researcher’s Personal wish and psychological need. What is needed now is more observation and more laboratory physics.
