# Grand Unification and Cosmology

## Abstract

Do cosmology and grand unified theories (GUTs) of elementary particle interactions have anything useful to say to each other? There is a great deal of theoretical work on GUTs unifying the strong, weak and electromagnetic interactions^{1}, now that many theorists perceive these individual interactions to be understood in principle. GUTs invoke energy scales of O(10^{15}) GeV which seem vertiginous to many physicists. It is not imaginable to reach these energies in laboratory experiments, and experimentalists are therefore forced to look for very indirect and feeble side-effects of grand unification such as proton decay. Even these valiant efforts may be brought to nought by a (logarithmically) modest increase in the grand unification mass-scale^{2}. However, this mass-scale may be achieved directly in cosmological and astrophysical situations. For example, black hole explosions could in principle achieve temperatures up to the Planck temperature of 10^{32°}K corresponding to energies of 10^{19} GeV, while temperatures corresponding to particle energies of 10^{15} GeV or more are generally thought to have occurred very early in the Big Bang when the Universe was about 10^{−37} seconds old.

### Keywords

Entropy Microwave Anisotropy Coherence Sine## Preview

Unable to display preview. Download preview PDF.

### References

- 1.J.C. Pati and A. Salam, Phys. Rev. Letters 31 (1973) 661 and Phys. Rev. D8 (1973) 1240 were the first proposers of grand unified gauge theories, but the type discussed in this paper was first proposed by H. Georgi and S.L. Glashow, Phys. Rev. Letters 32 (1974) 438.ADSCrossRefGoogle Scholar
- 2.J. Ellis, M.K. Gaillard, D.V. Nanopoulos and S. Rudaz — LAPP preprint TH-14/CERN preprint TH.2833 (1980) and references therein.Google Scholar
- 3.J. Learned, F. Reines and A. Soni, Phys. Rev. Letters 43 (1979) 907 and H.R. Steinberg, private communication (1980), quote limits on the nucleon lifetime of 2 and 3 x 10
^{30}years, respectively, if the decay modes resemble those expected in the SU(5) model of Ref. 1.ADSCrossRefGoogle Scholar - 4.H. Georgi, H.R. Quinn and S. Weinberg, Phys. Rev. Letters 33 (1974) 451.ADSCrossRefGoogle Scholar
- 5.A.J. Buras, J. Ellis, M.K. Gaillard and D.V. Nanopoulos, Nuclear Phys. B135 (1978) 66.ADSCrossRefGoogle Scholar
- 6.T. Goldman and D.A. Ross, Phys. Letters 84B (1979) 208 and Caltech preprint CALT-68-759 (1980).ADSCrossRefGoogle Scholar
- 7.W. Marciano, Phys. Rev. D20 (1979) 274 and Rockefeller Univ. preprint C00-2232B-195 (1980).ADSGoogle Scholar
- 8.L. Maiani, G. Parisi and R. Petronzio, Nuclear Phys. 136B (1978) 115 and references therein.ADSCrossRefGoogle Scholar
- 9.J. Ellis, M.K. Gaillard, L. Maiani and B. Zumino, LAPP preprint TH-15/CERN preprint TH-2841 (1980), contribution to these proceedings; p.69. J. Ellis, M.K. Gaillard and B. Zumino, CERN preprint TH.2842/ LAPP preprint TH-16 (1980) and references therein.Google Scholar
- 10.G. Steigman, Ann. Rev. Astron. and Astrophys. 14 (1976) 339.ADSCrossRefGoogle Scholar
- 11.G.’t Hooft, Nuclear Phys. B79 (1974) 276; A.M. Polyakov, JETP Letters 20 (1974) 194.MathSciNetADSCrossRefGoogle Scholar
- 12.J.P. Preskill, Phys. Rev. Letters 43 (1979) 1365; see also Ya.B. Zeldovich and M.Y. Khlopov, Phys. Letters 79B (1979) 239.ADSCrossRefGoogle Scholar
- 13.M.S. Chanowitz, J. Ellis and M.K. Gaillard, Nuclear Phys. B128 (1977) 506.ADSCrossRefGoogle Scholar
- 14.D.V. Nanopoulos and D.A. Ross, Nuclear Phys. B157 (1979) 273.ADSCrossRefGoogle Scholar
- 15.J. Yang, D.N. Schramm, G. Steigman and R.T. Rood, Ap.J. 227 (1979) 697; and G. Steigman, contribution to these proceedings, p. 495.ADSCrossRefGoogle Scholar
- 16.A.D. Sakharov,
*Pis’ma Zh.Eksp.Teor.Fiz*. 5 (1967) 32; A. Yu. Ignatiev, N.V. Krosnikov, V.A. Kuzmin and A. N. Tavkhelidze, Phys. Letters 76B (1978) 436; M. Yoshimura, Phys. Rev. Letters 41 (1978) 381; 42 (1979) 746(E). S. Dimopoulos and L. Susskind, Phys. Rev. D18 (1978) 4500; D. Toussaint, S.B. Treiman, F. Wilczek and A. Zee, Phys. Rev. D19 (1979) 1036; J. Ellis, M.K. Gaillard and D.V. Nanopoulos, Phys. Letters 80B (1979) 360, 82B (1979) 464(E), S. Weinberg, Phys. Rev. Letters 42 (1979) 850. A.D. Sakharov, Zh.Eksp.Teor.Fiz. 76 (1979) 1172; S. Dimopoulos and L. Susskind, Phys. Letters 81B (1979) 416; M. Yoshimura, Phys. Letters 88B (1979) 294.Google Scholar - 17.E.W. Kolb and S. Wolfram, Phys. Letters 91B (1980) 217, and 490 Caltech preprint OAP-579/CALT-68-754 (1979); J. N. Fry, K.A. Olive and M.S. Turner, Enrico Fermi Institute preprint 80-07 (198).ADSCrossRefGoogle Scholar
- 18.D.V. Nanopoulos and S. Weinberg, Phys. Rev. D20 (1979) 2484; S. Barr, G. Segré and A. Weldon, Phys. Rev. D20 (1979) 2494; see also J. Ellis, M.K. Gaillard and D.V. Nanopoulos, Ref. 16.ADSGoogle Scholar
- 19.Another cosmological topic worth mentioning is the lepton number of the Universe. If lepton number L is violated as well as B, then one might expect a net nL comparable with nB. In many GUTs however, B-L is conserved or very nearly so, and in these models neither ng nor nL has good reason to be small unless the net nB and nL were both initially zero (a symmetric Universe). In more general theories, where (B-L) is violated, this problem does not arise. For discussions, see S. Dimopoulos and G. Feinberg, Phys. Rev. D20 (1979) 1283; D.V. Nanopoulos, D. Stherland and A. Yildiz, Harvard Univ. preprint HUTP 79/A038 (1979), (to be published in Lettere al Nuovo Cimento). D.N. Schramm and G. Steigman, Phys. Letters 87B (1979) 141.Google Scholar
- 20.J. Ellis, M.K. Gaillard and D.V. Nanopoulos, Phys. Letters 90B (1980) 253.ADSCrossRefGoogle Scholar
- 21.W.H. Press, Physica Scripta 21 (1980) 702.ADSCrossRefGoogle Scholar
- 22.A. Guth and S.-H.H. Tye, Phys. Rev. Letters 44 (1980) 631; M.B. Einhorn, D.L. Stein and D. Toussaint, Univ. of Michigan preprint UM HE 80 - 1 (1980).Google Scholar
- 23.G. Lazarides and Q. Shafi, CERN preprint TH-2821 (1980).Google Scholar
- 24.For reviews of the cosmological monopole problem, see M.B. Einhorn, contribution to these proceedings, p. 569, and S.-H.H. Tye, Cornell University preprint “Monopoles, Phase Transitions and the Early Universe” (1980).Google Scholar
- 25.F.A. Bais, S. Rudaz, CERN preprint TH. 2885 (1980).Google Scholar
- 26.S. Weinberg, “Gravitation and Cosmology” ( Wiley, New York, 1972 ).Google Scholar
- 27.For GUTs based on bigger groups than SU(5), see R. Barbieri, D.V. Nanopoulos, J.C. Pati, B. Stech, contributions to these proceedings.Google Scholar
- 28.J. Ellis, M.K. Gaillard and D.V. Nanopoulos,Phys. Letters 80B (1979) 320.ADSGoogle Scholar
- 29.E. Gildener, Phys. Rev. D14 (1976) 1667; see also J. Ellis, M.K. Gaillard, A. Peterman and C.T. Sachrajda, Nuclear Phys. B164 (1980) 253, and references therein.ADSGoogle Scholar
- 30.P. Binétruy and T. Schücker, CERN preprint TH-2857 (1980).Google Scholar
- 31.K.T. Mahanthappa and M.A. Sher, Colorado preprint COLO-HEP 13 (1979).Google Scholar
- 32.L. Sulak and E. Bellotti, contributions to these proceedings, pp. 641, 675.Google Scholar
- 33.U. Amaldi, Proc. Neutrino 1979, Bergen, eds A. Haatuft and C. Jarlskog (Univ. of Bergen, 1979), p. 376; F. Dydak, Proc. EPS Int. Conf. on High Energy Phys., Geneva (1979) (CERN, 1979) p. 25; K. Winter, Proc. 1979 Int. Symp. on Lepton and Photon Interactions at High Energies, eds T.B.W. Kirk and H.D.I. Abarbanel ( FNAL, Batavia, 1980 ), p. 258.Google Scholar
- 34.R. Barbieri, CERN preprint TH.2850 (1980), contribution to these proceedings. p. 17.Google Scholar
- 35.For a recent review, see J.N. Bahcall, contribution to Int. Conf. on Astrophysics and Elementary Particles, Common Problems, Rome (1980).Google Scholar
- 36.Since this talk was given more information has become available about possible neutrino masses and oscillations: F. Reines, H.W. Sobel and E. Pasierb, U.C. Irvine preprint “Evidence for Neutrino Instability” (1980). E.F. Tretyakov et al., reportedly see a ye mass between 14 and 46 eV, while the,e /// induced event ratio in the 1979 CERN beam dump experiments was not unity; see also H. Wachsmuth, Proc. 1979 Int. Symp. on Lepton and Photon Interactions at High Energies, eds T.B.W. Kirk and H.D.I. Abarbanel ( FNAL, Batavia, 1980 ), p. 541.Google Scholar
- 37.G. Steigman, contribution to these proceedings, p. 495,Google Scholar
- 38.R.L. Golden et al., Phys. Rev. Letters 43 (1979) 1196.ADSCrossRefGoogle Scholar
- 39.R.L. Omnès, Phys. Rev. Letters 23 (1969) 38 and Astron. And Astrophys. 10 (1971) 228.ADSMATHCrossRefGoogle Scholar
- 40.See in particular D. Toussaint et al., and S. Weinberg, Ref. 16.Google Scholar
- 41.See E.W. Kolb and S. Wolfram, Ref. 17.Google Scholar
- 42.See J. Ellis, M.K. Gaillard and D.V. Nanopoulos, Ref. 16.Google Scholar
- 43.See the second paper of S. Dimopoulos and L. Susskind, Ref. 16.Google Scholar
- 44.D.V. NanopouloS and S. Weinberg, Ref. 18.Google Scholar
- 45.For an estimate of the dilution of the baryon number generated due to subsequent entropy generation in a homogeneous and isotropic Universe, see G. Steigman, K.A. Olive and D.N. Schramm, Phys. Rev. Letters 43 (1979) 239.Google Scholar
- 46.D.V. Nanopoulos, Phys. Letters 91B (1980) 67, discusses anthropocentric constraints on the baryon number asymmetry.ADSCrossRefGoogle Scholar
- 47.S.B. Treiman and F. Wilczek, Princeton preprint “Thermalization of Baryon Asymmetry” (1980).Google Scholar
- 48.M.S. Turner and D.N. Schramm, Nature 279 (1979) 303; M.S. Turner, Nature 281 (1979) 549, and Phys. Letters 89B (1979) 155; B. J. Carr and M.S. Turner, Enrico Fermi Institute preprint 80-09 (1980); see also D. Toussaint et al., Ref. 16.ADSCrossRefGoogle Scholar
- 49.J. Ellis and G. Steigman, Phys. Letters 89B (1980) 186; J.J. Aly, Mon.Not.Roy.Astr.Soc. 189 (1979) 479 points out that the Universe could have been very chaotic initially, as long as it smoothed out before the baryon asymmetry
^{16}was generated.ADSCrossRefGoogle Scholar - 50.J.M. Stewart, “Non-equilibrium Relativistic Kinetic Theory”, Lecture Notes in Physics, Vol. 10 (Springer, Berlin, 1971); C. Marie, Ann.Inst.H. Poincaré 10 (1969) 67, 127. It should be noted that the numerical factors of order 1 in the formulae for n and x used in Ref. 20 in fact depend on the precise angular form of the cross-section a being used, and that some formulae given in the literature are not exactly correct. See for some clarification N. Straumann, Helvetica Phys. Acta 49 (1976) 269. A1 so the exponent in formula (24) of Ref. 20 should be a factor of 2 larger. We thank N. Straumann for correspondence and discussions on these points. It has recently been emphasized by H. Sato, Kyoto University preprint RIFP-390 (1980) that the conventional viscosity approximation for discussing dissipative effects is only valid when T < t. In our case (38) this is only strictly valid when the temperature is in the lower part of the range 10
^{19}GeV > T > 10^{15}GeV. This means that the results of Ref. 20 can only be regarded as qualitative. However, we believe that the basic physical picture of Fig. 8 remains valid even if T > t: the point is that particles are then able to “leak” out of an inhomogeneity.Google Scholar - 51.A.F. Grillo, Frascati preprint LNF-80/21(P) (1980).Google Scholar
- 52.T.W.B. Kibble, J. Phys. A9 (1976) 1387 and M.B. Einhorn, D.L. Stein and D. Toussaint, Ref. 22.ADSGoogle Scholar
- 53.A. Guth, private communication (1980). For a recent review of cosmological phase transitions, their problems and implications, see T.W.B. Kibble, Imperial College London preprint ICTP/79-80/23 (1980). For discussions of the nature of the grand unified phase transition, see P. Ginsparg, CEN Saclay preprint DPh-T/80/27 (1980); M. Daniel and C.E. Vayonakis, CERN preprint TH-2860 (1980).Google Scholar
- 54.V.L. Ginzburg, Fiz.Teor.Tela 2 (1960) 2031.MathSciNetGoogle Scholar
- 55.G. Lazarides, M. Magg and Q. Shafi, CERN preprint 2856 (1980).Google Scholar
- 56.P. Langacker and S.-Y. Pi, Princeton Institute for Advanced Study preprint “Magnetic Monopoles in Grand Unified Theories” (1980) propose to reduce the cosmological density of monopoles by having electromagnetic gauge invariance spontaneously broken at temperatures T e. 1 TeV. Open problems in their scenario include its successful embedding in a grand unified theory, and the computation of the net charge density of the Universe due to C-, CP- and Q-violating effects out of thermal equilibrium. However, all other GUTs conserve Q and hence do not explain why the present charge density of the Universe is so small.Google Scholar
- 57.G. Barbiellini et al., DESY preprint 80/42 “Quarks and Monopoles at LEP” (1980) contains a review of monopole searches.Google Scholar