[Part 2: Physical Sciences] || Old and New Relics in Cosmology (A Review)

Old and New Relics in Cosmology (A Review)Author(s): Frank WilczekSource: Proceedings of the National Academy of Sciences of the United States of America,Vol. 79, No. 10, [Part 2: Physical Sciences] (May 15, 1982), pp. 3376-3379Published by: National Academy of SciencesStable URL: http://www.jstor.org/stable/12419 .

Accessed: 08/05/2014 10:31

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Academy of Sciences is collaborating with JSTOR to digitize, preserve and extend access toProceedings of the National Academy of Sciences of the United States of America.

http://www.jstor.org

This content downloaded from 169.229.32.137 on Thu, 8 May 2014 10:31:59 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=nas

http://www.jstor.org/stable/12419?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Proc. Natl. Acad. Sci. USA Vol. 79, pp. 3376-3379, May 1982 Review

Old and new relics in cosmology (A Review) FRANK WILCZEK

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

Communicated by Daniel E. Koshland, Jr., January 26, 1982

ABSTRACT Deep connections have been found between cosmology and elementary particle physics.

"Big Bang" cosmology (for reviews, see refs. 1 and 2) leads us to suspect that the Universe has expanded from a much hotter, denser phase. In standard cosmological models the temperature becomes arbitrarily high for times very near the Big Bang. The description of matter at extremely high temperature ultimately enters into the domain of elementary particle physics. In this way, cosmology, the science of the very largest structures in the Universe, makes contact with elementary particle physics, the science of the very smallest structures.

Description of the state of the Universe at times very near the Big Bang would not be a scientific enterprise if we could not make contact with presently observable realities. For this reason scientific cosmology is dominated by a search for relics. As we shall see, there are indeed a few relics from the very early universe that we can identify today. By checking whether the observed relics are reproduced, we can test theories of the be- havior of matter at high energies-thereby using the Universe as a high-energy laboratory.

CLASSICAL RELICS

Hubble Expansion. The earliest indication for Big Bang cosmology was the discovery of the recession of distant galaxies by Hubble in the 1920s. Distant galaxies were found to be moving away from us at a rate proportional to their distance:

v = Hr. [1]

The speed of recession is readily measured from the red-shift of spectral lines, but the determination of cosmic distances is a delicate problem and the "observed" value of H has changed by an order of magnitude over the years. Recently, another re- vision has been proposed (see ref. 3); at present the most it seems safe to conclude is:

50 km/sec per Mpc ' H ' 100 km/sec per Mpc [2]

in which Mpc is 1 megaparsec or 3 x 1024 cm. The form 1 of the Hubble law is profoundly significant. If the universe is to be uniform-homogeneous and isotropic-on large scales at all times, then the only allowed change in its spatial structure is an overall change of scale. As is readily seen, such changes are of the form 1 and, conversely, an expansion of the form 1 keeps an initially uniform Universe uniform at later times.

Extrapolating the form 1 backward in time, imagining H(t) to be constant, we find convergence of all galaxies to a point at time 1/H. This is obviously suggestive of a Big Bang picture, with 1/H now identified as the age of the Universe. In reality, as I shall discuss, H is not expected to be quite constant, but the present 1/H does set the scale for the age of the Universe. Numerically,

1010 yr : H-1 s 2 x 1010 yr. [3]

3 K Microwave Background. At temperatures above 10 K the Universe would be filled with electrons, nuclei, and photons (black-body radiation) in thermal equilibrium. In the Big Bang theory, these conditions occurred for t ' 105 yr after the Big Bang at t = 0. As the Universe expanded and cooled slightly below this temperature, the electrons and nuclei combined into electrically neutral atoms. The neutral atoms couple only weakly to the photons, so since this time the atoms and photons have coexisted as two essentially independent gases filling the Universe.

An isotropic background of microwave radiation was discovered experimentally in 1964 (4, 5). Subsequent measurements have confirmed the isotropy to a high degree (1 10-3 variations in intensity with angle) and the thermal character of the radiation (for recent ideas and results on the microwave background, see refs. 6 and 7). Both these characteristics lead us to identify the observed microwave background as a relic of the Big Bang.

As observed at present, the temperature of the photon gas is -2.7 K. The change from x-rays at 104 K to microwaves at 2.7 K can be considered as an example of the Doppler effect on a grand scale-the sources that originally produced the x- rays about 10 billion years ago are now receding from us at very nearly the speed of light!

The observed isotropy of the background radiation provides the strongest direct support for the generalized Copernican as- sumption of a homogeneous, isotropic universe.

Nuclear Abundances. At even higher temperatures, '1010 K, protons and neutrons were present as free particles, not bound into nuclei. These conditions occurred at t ' 200 sec. As the Universe expanded and cooled, the protons and neutrons combined into nuclei. In fact, to a first approximation, what happened is simply that all the available neutrons combined with protons into 4He nuclei, by chains such as n + p -2H + y, 2H + 2H-* 3H + p, 3H + d -_ 4He + p. Heavier nuclei were not produced in significant quantities due to the lack of a stable nucleus with five or eight nucleons (Coulomb barriers also inhibit the 4He nuclei from fusing with one another). In- complete "cooking" may have left some 2H and 3He as well (8, 9).

This picture explains qualitatively why the overwhelming majority (99%) of nuclei in the Universe are H or 4He. It is gen- erally believed that heavier elements are produced not cosmologically but rather are produced inside stars and are lib- erated in supernova explosions.

To account quantitatively for the abundance ratio of 4He/ H, according to these considerations the crucial parameter is the relative abundance of protons and neutrons at t 200 sec when they began to combine. Here enters the first, now classical, application of particle physics in cosmology. At temperatures '1010 K, weak interactions such as v + p - e+ + n, e- + p <-> v + n maintain a "chemical" equilibrium between p and n. As long as these reactions are common, the relative abundance of p and n can be calculated by ordinary statistical mechanics. p will be more common than n because it is lighter; the

3376



Review: Wilezek Proc. Natl. Acad. Sci. USA 79 (1982) 3377

abundance ratio N/P is given essentially by the Boltzmann fac- tor N/P = ec/T, A = m- mp. As the temperature cools past a critical temperature (T*), --,:'101o K, the density and energy of the neutrinos and electrons (likewise calculable from statistical mechanics) become too small to maintain equilibrium and the N/P is thereafter approximately constant, "frozen in. " Detailed numerical calculations based on these ideas have been carried out, with striking success. The predicted ratio of approximately 25% 4He by weight is found to hold in a number of astrophysical environments where contamination by material processed in stellar interiors should be small (see the debate in refs. 10 and 11 and the references therein).

Will the Expansion Continue Forever? Another relic of a somewhat different nature concerns the overall balance between the present expansion of the Universe and the gravitational attraction between its parts, which slows the expansion. Will the expansion continue forever, or will it eventually halt and reverse, leading to a Big Crunch?

There is no fully satisfactory theoretical approach to this question at present. In the cosmological equations of general relativity an integration constant appears which determines the answer. This integration constant must at present be taken from experiment and constitutes another, peculiar, relic of the early universe.

There are several sorts of observations relevant to our question.

(i) The change in the rate of expansion can be measured directly by determining how the Hubble parameter changes in time. This is done in practice by taking advantage of the time lag induced by the finite speed of light. Our telescopes are now receiving images of very distant objects which show those objects in their past. Changes with H in time will affect the velocity-distance relationship, Eq. 1, for such objects. This can be observed as curvature in plots of recession velocity v versus distance r for large r. Observations are conventionally sum-

d marized in the deceleration parameter qo dt H-1 - 1. For

free expansion, Hcx llt (in Eq. 1, r grows while v is constant) so q0 = 0; because gravity slows the expansion we certainly expect q0 > 0. More detailed considerations show that q0 = /2 is the critical value-if q0 > 1/2 the universe will eventually collapse; if q0 < 1/2 expansion continues forever. Unfortunately, the same difficulty in calibrating distances that contaminates the determination of H also plagues measurements of q0. At present it seems safe to conclude no more than q0 o 5 from these optical observations. The space telescope may make a great contribu- tion in sharpening the optical measurements of H and q0 (for an interesting proposal to use supernova observations, see ref. 12).

(ii) There is a close relationship between q0 and the age of the Universe. If the expansion is slowing rapidly, then it was more rapid in the past and it takes a shorter time to arrive where we are today. Small values for the age of the universe signify eventual collapse. Quantitatively, the relationship is

tn- 3 H2 -V2q0 _ 1 3/2|C o2 - [4] tfOW= H 12q0 - ii 2q0

where C1 --cosh-' for q0 < 1/2 and C-' cos-1 for q0 > 1/2. This formula unfortunately is not very transparent, especially because of its apparent (not real) singularity at q0 = 1/2. The important qualitative points are that the overall scale for the age of the Universe is indeed W'1 as we anticipated before, that at the critical value q0 = 1/2 we find tno = 2/3H'1, and that in all cases (q0 > 0!) tno S W'. If the Universe is younger than

2/3H-' it is fated to collapse eventually; if not, it will expand forever.

Two main types of observations are relevant to the question of the age of the Universe. 235U and 238U are believed to be produced in supernova explosions in the ratio 1.6:1. The present relative rarity of 235U is due of course to its radioactive instability on cosmological time scales. Measurements of "5U abundance in uranium samples allow us to estimate the time it has had to decay. From these measurements and similar techniques applied to other isotopes, one finds t.., - 9 x 109 yr (13). [There are reasons to think that most uranium was formed early in the history of the galaxy (14); in this case the value determined here is not only a lower bound to the age of the universe but also a good estimate of its actual value!] Stellar evolution theory may be used to estimate the ages of stellar populations in glob- ular clusters (15). Large, bright stars burn out more quickly than do smaller, dim stars. By studying clusters we can observe how bright are the brightest stars that still shine normally and then date the cluster by theoretically estimating how long the slightly brighter stars have taken to burn out. In this way, typical ages of 8-15 x 109 yr have emerged.

It is very satisfying that both the radioactive and stellar evolution dating procedures lead to ages quite comparable to but less than H-'. This is a further indication of the inner consis- tency of Big Bang cosmology. Comparing the numerical values for the critical age 6.7 x 109 yr < 2/3H-1 < 13 x 109 yr, we find that age measurements are not quite sufficient to settle the question of whether there will be a Big Crunch but, if the Hub- ble parameter H turns out to be at the high end of its present range, eternal expansion will be favored.

(iii) The relative strength of gravitational attraction of course depends directly on the mass density p. The critical density is

3H2 PC = 8irG [5]

which numerically is 1-4 x 10-29 g/cm3. Larger densities will give a Crunch; smaller densities will give eternal expansion. Estimating the number of different types of stars from their observed luminosity and multiplying by the appropriate stellar masses, we find that the total mass in visible stars is about pvi, = 0.03 pc. Recently, there have been exciting indications for substantial amounts of nonluminous matter (16); I shall discuss this further below.

NEW RELICS Neutrino Background. At temperatures - 10" K, neutrinos

are readily produced and destroyed in weak interactions like e+e- vi-. Because both weak interaction cross sections and the equilibrium density of particles decrease rapidly with temperature, as the Universe expands and cools such interactions become unlikely at lower temperatures. For T < 1010 K the neutrinos form an inert cosmological background, similar to the photon background discussed above.

Knowing the photon density, by using statistical mechanical arguments one can predict the neutrino density to be

nV+ := 160/cm3, per species [6]

where the species are electron, muon, r lepton, . . ., neutrinos. Although these neutrinos do not significantly interact in the

ordinary sense with other matter, their gravitational influence can be very important. In the first place, if the neutrinos have a small mass m, then they contribute the mass density

p = 2 vn = Emvi(eV)pJ/65h2 [7] species ii



3378 Review: Wilezek Proc. Nati. Acad. Sci. USA 79 (1982)

where H-h x 100 km/sec per Mpc. Assuming, in line with the evidence of the classical relics, that p - 2p, we find 1i m,,I < 130h2. This cosmological limit compares very favorably with the laboratory limits mive n, 60 eV, mVi-,, - 6 x 105 eV, and mVT - 2 X 108 eV. As I shall discuss below (The Allure of Massive Neu- trinos), there are reasons to believe that the neutrinos may ac- tually have a nonvanishing mass of the order of a few electronvolts and dominate the mass density of the present Universe.

Nucleosynthesis Revisited. As discussed above, the primor- dial density of 'He relative to H nuclei is determined by the ratio of n to p nucleons when these combine at T 109 K. This ratio in turn is determined by how long the reactions v + p <-> e+ + n, e- + p <-> v + n can maintain chemical equilibrium between the protons and neutrons. The equilibrium density ratio N/P - e-(mn-mP)/T decreases as T decreases, so that the lower the temperatures for which equilibrium is maintained, the fewer neutrons there will be and the lower the 'He abundance will be. How well chemical equilibrium is maintained is governed by a competition between the mean time between the relevant collisions and the rate of expansion of the Universe. The faster the expansion, (i) the more difficult it will be to maintain equilibrium, (ii) the higher the effective temperature at which the N/P abundance is frozen in, and, finally, (iii) the more 4He.

What does all this have to do with neutrinos? The rate of expansion at the temperatures relevant to nucleosynthesis tends to increase as the number of different species of neutrinos increases. (One can see this by imagining running the Universe backward in time starting from the present-we then have a collapse whose rate increases with the more stuff there is at a given temperature!) The successful calculations of 4He abundance alluded to above assume that the three observed species of neutrinos-ye, v,., and v,-exhaust the list. If there were five or more neutrino species, the modified calculations would yield a dangerously large prediction for the present 4He abundance (17).

It should be possible to test this remarkable cosmological constraint on particle physics in the near future. The lifetime of the Z boson depends sensitively on the number of neutrino species (because Z -* mv is a major decay mode) and should be measureable at high energy e+-e- colliders.

The Allure of Massive Neutrinos. There is impressive ob- servational evidence for large quantities of nonluminous matter in the Universe. By measuring Doppler shifts in the 21-cm line ofhydrogen clouds orbiting around galaxies, one may determine the orbital speed of these clouds (18, 19). If the matter in the galaxy were concentrated in its optically bright region, then according to Kepler's law the orbital velocity for clouds outside the bright region would vary with the radial distance as v(r) oc r-12. Instead it is found that, for most galaxies studied, v(r) becomes essentially constant (clouds at distances up to 40 kpc have been observed; in comparison, the luminous matter extends only to 10 kpc). These measurements indicate the presence of a nonluminous component to the galactic mass distribution, with density p(r) o 1/r2. Another indication for large amounts of dark matter comes from the study of rich clusters of galaxies. These galaxies appear to form gravitationally bound systems to which the virial theorem relating kinetic to gravitational poten- tial energies can be applied. It is found that, to satisfy the virial theorem, 10-50 times more mass must be present in the cluster than would be inferred from its luminous (stellar) matter.

A main question of cosmology is then: What is this dark matter, and does it provide sufficient mass to make the Universe collapse?

An important constraint on the form of this mass comes from recent detailed studies of nucleosynthesis. Although the great

majority of neutrons combine into 4He in the early universe, the nuclear reaction chains will not be completely efficient and some intermediate products including 2H and 3He will be produced too. The amount of 2H and 3He produced depends sensitively on the density of nucleons at the time when they fused. Higher density means more efficient nuclear burning and hence less 2H and 3He. On this basis, it has been concluded* that the density of matter in nucleons cannot be too large: P ' 0.06p,. If this is correct, it rules out the otherwise not un- reasonable hypothesis that the dark matter might be in the form of nonluminous Jupiter-like objects (which of course would be made from nucleons).

The idea that neutrinos might be massive has become very attractive with the development of unified gauge theories of particle interactions, and cosmologically interesting masses of the order of tens of electronvolts are not implausible in this framework (ref. 20 and references therein). A large number of experiments designed to detect such masses have been done and many more are in the planning stages. So far, the results have been negative or inconclusive, with one possible exception (21). Unfortunately, the most plausible possibility-that it is only the neutrino v, associated with the recently discovered - lepton that has appreciable mass-is particularly difficult to address experimentally.

Galaxy Formation. Although the microwave background is exceedingly isotropic, this is not the case for the distribution of ordinary matter. Even on large scales we have clumping of matter first into galaxies and then into clusters and superclusters. It is averaged over the largest scales (of order 1,/oth the size of the visible universe), if then, that the distribution of galaxies seems reasonably uniform (22).

Particle physics considerations seem to sharpen the problem of galaxy formation. If the amount of matter per photon is really fixed locally to a universal value by microphysical parameters, as I shall suggest in the next section, then the observed isotropy of the microwave background tells us that, until the time when nuclei and electrons combined into electrically neutral atoms, the nuclei were very uniformly distributed also. Charged particles have a difficult time moving through the photon sea; it is like a viscous medium for them, so that fluctuations in the density of nuclei could not grow by gravitational instability until after they combined into atoms. We then have to ask: Can small fluctuations at the combination time grow fast enough to form galaxies and clusters as observed?

Detailed analyses of this problem seem to indicate that this can occur only if the total mass density is close to p, The problem is especially eased if the mass is in neutrinos, because fluctuations in neutrino density can start growing by gravitational instability prior to combination and the nucleons then "fall in" to these fluctuations after combination.t

This kind of picture, wherein neutrino fluctuations provide the seeds for the observed inhomogeneity of the matter distribution, has another important consequence. Because the neutrinos essentially do not interact except gravitationally (for T S 1010 K), inhomogeneities in the neutrino density on too small a scale will simply diffuse away. It is only for very-large-scale fluctuations that gravitational interactions can hold the fluctuations together and indeed lead to their growth. This leads to the Blini (Russian pancake) theory of galaxy formation, wherein the basic fluctuations are on the scale of superclusters of galaxies and collapse into sheets which then fragment into

* Steigmann, G., "Particles and Fields," presented at American Phys- ical Society meeting, Santa Cruz, CA, 1980.

t Doroshkevich, at 11th Texas Symposium on Relativistic Astrophysics (to be published).



Review: Wilezek Proc. Natl. Acad. Sci. USA 79 (1982) 3379

smaller clusters. Very recent observations (23) may indicate that there are large regions ("holes in the sky") of the Universe con- taining very few galaxies, which certainly would be suggestive of organization of galaxies into two-dimensional sheets or Blini.

Matter-Antimatter Asymmetry. Perhaps the most striking application of new ideas in particle physics to cosmology is the development of an explanation of the asymmetry between matter and antimatter in the Universe (for a semipopular account, see ref. 24). This is that, although the laws of physics are very nearly symmetrical between matter and antimatter, the Uni- verse appears to contain essentially only the former.

The relic we wish to explain here is the ratio of baryon number density to photon density, which is observed to be about

r = nB/n, , 10-10. [8]

This ratio is essentially constant through the history of the Universe, as long as baryon number B is conserved and the expansion of the Universe is slow enough to be essentially adiabatic. Because the entropy in the photon gas is proportional to the number of photons, in an adiabatic process the number of photons is conserved. Nonadiabatic processes increase the photon density. The value of r therefore has been "frozen in" (or decreasing) since the time, if ever, when baryon number nonconserving processes were significant.

It was realized some time ago, notably by Sakharov (25), that if we had baryon number-violating processes that also were not symmetrical between particles and antiparticles (violating charge-conjugation symmetry C and its generalization CP) then nonequilibrium processes in the early Universe could generate a non-zero net baryon excess (see also ref. 26). Each qualifi- cation in the previous sentence is necessary-that is, we must have violation of baryon conservation, C and CP invariance, and also get well out of thermal equilibrium before an asymmetry between matter and antimatter can develop.

These ideas were rediscovered (27-29) independently by several groups in 1978, with the new element that in the mean- time developments within particle physics had generated fairly definite expectations that baryon conservation is indeed vio- lated (30). Unified theories of the strong, electromagnetic, and weak interactions in their simplest and most attractive form re- quire the existence of particles with mass 10O' times that of the proton whose exchange or decay can violate baryon number.

In the framework of these theories, at temperatures 31022 K, baryon number-violating interactions were significant and chemical equilibrium could be maintained despite the rapid expansion of the Universe-so at this time nB = 0. As the temperature cooled past this range, equilibrium could not be maintained and, after a brief time when B baryon number violating was significant but not sufficient to maintain equilibrium, r = nB/n,, was frozen in. Several quantitative calculations of r have been attempted (30-33) and, although there are severe uncertainties in several relevant parameters, the results indicate that r 10-10 as observed is a not implausible outcome.

The key element in these speculations is of course that baryon number-violating processes really do occur. The unified theories alluded to above predict that the proton and other otherwise stable nuclei can decay by baryon number-violating processes with a lifetime p 1030?2 yr. A first indication of this may be the experiments of Krishnaswamy et al. (34).

CONCLUSION The foregoing has been a summary of the better established parts of our subject. Other interesting ideas and puzzles abound-why is the density of the Universe at all close to critical (for some interesting ideas along this line, see ref. 35), why is the gravitational energy of the vacuum so small, . . . ? There is also a large literature placing bounds on properties of particles (e.g., possible decays of neutrinos into photons and other particles) which would lead to consequences contrary to astrophysical observations (in this example, an extra cosmological background of energetic photons) (e. g., ref. 36).

In conclusion I would like to reemphasize that, to be fruitful, speculation about the early Universe must make contact with observable realities. For that reason, new experimental results on neutrino masses, proton decay, holes in the sky, small an- isotropies in the microwave background, and more precise indications of H and the density of the Universe are eagerly anticipated. 1. Silk, J. (1980) The Big Bang (Freeman, San Francisco). 2. Weinberg, S. (1972) Gravitation and Cosmology (Wiley, New

York). 3. Hodge, P. (1981) Annu. Rev. Astron. Astrophys. 19, 357. 4. Penzias, A. & Wilson, R. (1965) Ap. J. 142, 419. 5. Dicke, R., Peebles, P. J., Roll, P. & Wilkinson, D. (1965) Ap. J.

142, 414. 6. Weiss, R. (1980) Annu. Rev. Astron. Astrophys. 18, 489. 7. Sunyaev, R. & Zeldovich, Ya. (1980) Annu. Rev. Astron. Astro-

phys. 18, 537. 8. Peebles, P. J. (1966) Ap. J. 146, 542. 9. Wagoner, R., Fowler, W. & Hoyle, F. (1967) Ap. J. 148, 3. 10. Olive, K. & Turner, M. (1981) Phys. Rev. Lett. 46, 516. 11. Stecker, F. (1981) Phys. Rev. Lett. 46, 517. 12. Wagoner, R. (1979) Comments Astrophys. 8, 121. 13. Symbalisty, E. & Schramm, D. (1981) Rep. Prog. Phys. 44, 293. 14. Dicke, R. H. (1962) Ap. J. 155, 223. 15. Iben, I. & Rood, R. (1970) Ap. J. 159, 605. 16. Faber, S. & Gallagher, J. (1979) Annu. Rev. Astron. Astrophys.

17, 135. 17. Yang, J. et al. (1979) Ap. J. 227, 697. 18. Rubin, V., Ford, W. & Thonnard, N. (1978) Ap. J. L107. 19. Krumm, N. & Salpeter, E. (1979) Ap.. 84, 1138. 20. Langacker, P. (1981) Phys. Rep. 72, 185. 21. Lubimov, V., Novikov, E., Nozik, V., Tretyakov, E. & Kosik, V.

(1980) Phys. Lett. B. 94, 266. 22. Peebles, P. J. (1980) The Large-Scale Structure of the Universe

(Princeton Univ. Press, Princeton, NJ). 23. Kirshner, R., Oemler, A., Schechter, P. & Shectman, S. (1981)

Ap. J. 248, L57. 24. Wilezek, F. (1980) Sci. Am. 243, no. 6, 82. 25. Sakharov, A. (1967) JETP Lett. 5, 27. 26. Ignatiev, A., Krasnikov, N., Kuzmin, V. & Tavkhelitze, A. (1978)

Phys. Lett. B 76, 436. 27. Yoshimura, M. (1978) Phys. Rev. Lett. 41, 281. 28. Dimopoulos, S. & Susskind, L. (1979) Phys. Rev. D 18, 4500. 29. Toussaint, D., Treiman, S., Wilezek, F. & Zee, A. (1979) Phys.

Rev. D 19, 1036. 30. Weinberg, S. (1981) Sci. Am. 244, no. 6, 64. 31. Ellis, J., Gaillard, M. & Nanopoulos, D. (1978) Phys. Lett. B 80,

360. 32. Weinberg, S. (1979) Phys. Rev. Lett. 42, 850. 33. Barr, S., Segre, G. & Weldon, H. (1979) Phys. Rev. D 20, 2484. 34. Krishnaswamy, M., Menon, M., Mondal, N., Narasimham,V.,

Sreekantan, B., Ito, N., Kakawami, S., Hayashi, Y. & Miyake, S. (1981) Phys. Lett. B 106, 339.

35. Guth, A. (1981) Phys. Rev. D 23, 347. 36. Cowsik, R. (1977) Phys. Rev. Lett. 39, 784.



Documents

[Part 2: Physical Sciences] || Old and New Relics in Cosmology (A Review)