On Relativistic Cosmogony

REVIEWS OF MODERN PH YSICS VOLUME 21, NUMBER 3 J ULY, 1949 On . 4e. .ativistic Cosmogony G. GAMow The George WashingtorI, University, TVashingtoe, D. C. 'q INSTEIN'S general theory of relativity received must be explained by some as yet unknown physical ~ brilliant con6rmation in the so-called "three phenomenon causing the reddening of light which tests:" advance of the perihelion of mercury, deflection travels over very large distances. However, except for of the light rays passing near the solar surface, and the the descriptive statement to the effect that "light gravitational shift of spectral lines in the light emitted quanta may get tired traveling such a long way, " no by the sun and some other stars. reasonable explanation of such a reddening has as yet These tests pertain, however, to one particular been proposed, and, as a matter of fact, can hardly be solution of the fundamental equations of gravitation expected on the basis of present ideas concerning the describing the local spherically symmetrical field which nature of light. Moreover, abolishing the idea of an surrounds a gravitating masspoint. expanding .universe, one would immediately lose the Another important solution of the same equations sound foundation for the interpretation of evolutionary corresponds to the case of uniform mass-distribution phenomena in astronomy, and it will be very difficult and is supposed to describe the geometry and time to answer such questions as to why the natural radio- behavior of the universe as a whole. The agreement active elements are still in existence, why the stars did of the cosmological consequences of general relativity not use up all hydrogen an eternity ago, etc. with observational evidence should give us additional According to Hubble's measurements, the rate of and more extensive proof of the correctness of basic uniform expansion (at the present time) is given by ideas of the theory, whereas any serious disagreement 1 dl cm would lead to the rather discouraging result that 18.10 17 cm. (&a) Einstein's theory of gravitation is applicable only to dt - present sec. local 6elds and fails when for description of used a Assuming that the expansion was linear in the past, larger regions of space. we find that it must have started 5.6 10"sec, =1.8 10' During the last decades there have appeared a num- years ago, so that at that epoch the material of the ber of the modi6cation of the proposals suggesting universe must have been in the state of very high of cosmo- original theory Einstein for the purposes of density and correspondingly high temperature. Al- include fundamental logical application. These the though the 6gure of 1.8 $0' years agrees in order of changes in the notion of time ' the assumption (Milne), magnitude with various astronomical and geological of variability of the gravitational constant ' (Dirac), estimates of the age of our universe, its exact value is and the introduction of a new phenomenon of creation certainly too low. In fact the study of radioactivity of of mass ' we (Jordan, Hoyle). In the present article rocks indicates quite definitely that the solid crust of will inter- intentionally disregard all such proposals, the earth must have existed for at least 2.5.10' years esting as since our aim here is see whether they are, to so that the age of the universe is probably closer to or the not problems of cosmology and cosmogony can 3.10' years. Since this discrepancy is certainly beyond "old fash- be understood entirely on the basis of the the limits of errors in the astronomical measurements ioned" general theory of relativity in its original form of the red shift, and since taking into account the eGect proposed by Einstein. of gravitational attraction between the galaxies during The first and the most conse- general cosmological the earlier expansion period, we will still further shorten quence of the Einstein theory is that our universe may (though only very little) the calculated age, it appears finite be either open and infinite, or and closed, and that we have here the 6rst serious disagreement between that it may either expand or contract with time. the conclusions of relativistic cosmology and the Hubble's discovery of the red shift in the spectra of observed facts. distant and its interpretation as the result of galaxies, This disagreement, however, can be removed by uniform the expansion of space, represents the 6rst considering the eGect of the so-called cosmological term relativ- direct confirmation of that basic conclusion of -in the general equation of the expanding universe. In istic cosmology. It. is true that some physicists and fact, the most general homogeneous and isotropic solu- astronon1ers prefer to believe that the observed red shift tion of the fundamental equatious of gravitation can is not due at all to mutual recession of galaxies, but be written in the form' E. A. Milne, Relativity, Gravitation and world Structure dl pS~G (Clarendon Press, Oxford, 1935); Ei'nematic Relativity (Clarendon pP cV+ P),——(1b) — Press, Oxford, 1948). dt 43 ' P. A. M. Dirac, Proc. Roy. Soc. 165, 198 (1938). 3) ' P. Jordan, Naturwiss 26, 417 (1938); Astr. Nachr. 276, 193 4 Cf. R. C. Tolman, Relativity, Thermodynamics, und Cosmology (1948); F. Hoyle, Nature 163, 196 (1949). (Clarendon Press, Oxford, 1934), pp. 396 and 404. 367 368 G. GA MOW so that we can write ' (3/A) *ln(l„„+Ll„„'—(3c'e'/A) )' =3 10' yr. =9.3 10"sec. (4) $otorotion The equation itself gives us cV A)* ( — '. + ) =1.8X10 "sec. 4J I X 3) ~o I Putting l~„,=10" cm (because p~„,=10 " g/cm'), e 0 and solving Eqs. (4) and (5) for e and A, we 6nd' Lal I- e=s 5.10' ~-2 ol P S=i)&5)&10"em= i&5X10' light years, and I- "4 K ' A. =8.6&(10 "sec. '. n„t = 0.81x10'e — 0-5 cm3 0 0 This result indicates that the space of the universe has -6 n&t~0.51 x 10 cm& a negative curvature and is therefore infinite in exten- &7 ~ sion, and also that the value of cosmological constant, -8 being different from zero, is still sufficiently small to be 0 50 100 150 200 250 ATOMIC WEIGHT of no importance in consideration of planetary motion in local 6elds. F&G. |.Calculated values of relative abundance of elements. Another extremely important method of comparing the consequences of relativistic cosmology with the where / is an arbitrary length in the expanding or observed properties of our universe is presented contracting space, e(= const. ) is the curvature radius S by Hubble's studies of the red shift and space density in expressed in terms of that length, p the total mass the case of very disturb galaxies. Since at these distances density (including matter and radiation), and A the it becomes impossible to resolve the galaxies into indi- cosmological constant. It is convenient for future vidual stars, distance determinations have to be carried discussion to attach a de6nite meaning to the length /, out exclusively on the basis of the observed apparent and we define l as the side of a cube containing one gram magnitudes of the galaxies themselves. The study of of matter (excluding the radiation). whose distances can be determined Rewriting Eq. (1) in the form nearby galaxies, by the observation of cepheides or bright stars, has shown & that their absolute magnitudes vary only very little, 1 dl (S~G cV A. q +—I, being distributed according to the Gauss law around a tdt 0 3 P 3) certain mean value. Consequently, one can expect that taking the mean apparent magnitude of many galaxies we notice that the present value of the left side is belonging to the same distant cluster, and using the given by the Hubble's constant: 1.8 10 '. Using also inverse square law for apparent luminosity, one should the Hubble's value 10 " (g/cm') for the present mean get a rather exact figure for their distance from us. density of the universe, we 6nd that the 6rst term The results of such a survey carried out by Hubble's under the radical must be negligibly small as compared brought him to the conclusion that: (a) at very large with the other two. ' Thus, assuming A. =O, we would distances the observed red shift begins to increase obtain a linear dependence of / on time for almost the faster then the distance, (b) at the same distances the would entire past history of the universe, and come to mean density of galaxies (i.e., the number of galaxies the erroneous conclusion that the expansion must have per unit volume) begins to increase with distance. Both started only 1.8 10' years ago. However, retaining the results are in apparent contradiction with the above- cosmological term, and ascribing to A. a de6nite positive stated conclusions of relativistic cosmology: in fact, value, we can easily fit the solution of (2) with the since when observing distant galaxies we are actually observed data. In fact, the above equation (with p=0) looking back into the past, we should expect to find can be integrated in the form lower rather than higher expansion velocities (the effect of positive A in the Eq. (2)). If this particular result t = (3/A)' ln —(3c'e'/h. $-*' {l+ $P ) I (3) of Hubble were actually correct, we would be forced to the conclusion that the age of the universe is even ' Since p increases rather fast with decreasing l, the first term becomes important during the early stages of expansion, which, 6 R.

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