Abstract
The matter content of an ever-expanding Friedmann universe will never become negligible compared with the radiation, assuming electrons and positrons (e±s) are absolutely stable, even if all other massive particles are unstable. The possible annihilation of e±s in a k = 0 model occurs so slowly that the radiation density can never greatly exceed the matter density. For a very homogeneous distribution of e±s which cool at just the expansion rate, the asymptotic ratio of matter to radiation density in a k = 0 universe is calculated here to be (√105−3)/12 = 0.6039. Heating by collisional recombination would probably keep the matter density far higher. A certain amount of clumping might make the annihilation occur faster, but larger inhomogeneities are likely to lead to black holes which could be even more effective in keeping the universe from becoming radiation dominated.
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References
Davies, P. C. W. Mon. Not. R. astr. Soc. 161, 1–5 (1973).
Islam, J. N. Q. Jl R. astr. Soc. 18, 3–8 (1977); Sky Telescope 57, 13–18 (1979).
Barrow, J. D. & Tipler, F. J. Nature 276, 453–459 (1978).
Dyson, F. J. Rev. mod. Phys. 51, 447–460 (1979).
Pati, J. C. & Salam, A. Phys. Rev. D8, 1240–1251 (1973); Phys. Rev. Lett. 31, 661–664 (1973).
Georgi, H. & Glashow, S. L. Phys. Rev. Lett. 32, 438–441 (1974).
Georgi, H., Quinn, H. R. & Weinberg, S. Phys. Rev. Lett. 33, 451–454 (1974).
Zel'dovich, Ya. B. Phys. Lett. 59A, 254 (1976); Soviet Phys. JETP 45, 9–11 (1977).
Hawking, S. W. Nature 248, 30–31 (1974); Commun. Math. Phys. 43, 199–220 (1975).
Bransden, B. H. Case Studies in Atomic Collision I (eds McDaniel, E. W. & McDowell, M. R. C.) (North-Holland, Amsterdam, 1969).
Kramers, H. A. Phil. Mag. 46, 836–871 (1923).
Thomson, J. J. Phil. Mag. 23, 449–457 (1912).
Percival, I. C. & Richards, D. Adv. atom. molec. Phys. 11, 1–82 (1975).
Carr, B. J. Astrophys. J. 201, 1–19 (1975).
Page, D. N. Phys. Rev. D16, 2402–2411 (1977).
Page, D. N. & McKee, M. R. Preprint (Pennsylvania State University, (1980).
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Page, D., McKee, M. Eternity matters. Nature 291, 44–45 (1981). https://doi.org/10.1038/291044a0
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DOI: https://doi.org/10.1038/291044a0
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