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Quantum Cosmology — The Story So Far

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Gravitation, Gauge Theories and the Early Universe

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 29))

Abstract

While commenting about the state of quantum gravity, Lee Smolin has said in 1979:1 “... while there has been a lot of interesting and imaginative work ... nothing which could be definitely called progress has been accomplished in this time — say, two decades ...”. In the course of this chapter, I will try to convince you that the situation remains just as bad today.

What is that, Lord, which being known, all these become known? — Mundako Upanishad.

‘A dream-child moving through a land of wonders wild and new, In friendly chat with a bird or beast-And half believe it true.’ — C. L. Dodgson (Lewis Caroll)

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Notes and References

  1. L. Smolin (1979), What is the problem of quantum gravity?, preprint based on part 1 of the thesis (Harvard University).

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  2. These questions, of course, are discussed in literature. Some good reviews of quantum gravity are by C. J. Isham, in Quantum Gravity I & II (eds. C. J. Isham, R. Penrose and D. W. Sciama; C.U.P., 1975,1980); J. A. Wheeler in Relativity, Groups and Topology (eds. B. S. De Witt and C. De Witt; Gordon and Breach, 1964); J. Hartle in The Very Early Universe (eds. G. W. Gibbons, S. W. Hawking, S. T. C. Silkos; Cambridge, 1983) and the various articles in Quantum Theory of Gravity (ed. S. Christensen, Adam Hilger, 1984).

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  3. E.g. G.’ t Hooft (1973), Nucl. Phys. B62, 444; S. Deser and P. Van Nieuwenhuizen (1974), Phys. Rev. D10, 401, 411.

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  4. T. Padmanabhan, T. R. Seshadri and T. P. Singh (1985) J. Mod. Phys. (to appear); K. Eppeley and E. Hannah (1977), Found. Phys. 7, 51; D. N. Page and C. D. Geilker (1981), Phys. Rev. Letts. 47, 979.

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  5. There are many good reviews on these subjects; for example, see P. Van Nieuwenhuizen (1983) Relativity, Groups and Topology, II’ (eds. B. S. De Witt and R. Stora; North-Holland); J. Scherk (1975), Rev. Mod. Phys. 47, 123; J. H. Schwarz (1982), Phys. Rep. 89, 223.

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  6. Some limited application of nonperturbative techniques in quantum gravity can be found in T. E. Tomboulis, Phys. Letts. 70B(1977), 361; 97B (1980), 77; L. Smolin, Nucl. Phys. B208(1982), 439; S. Weinberg (1979) in General Relativity — An Einstein Centenary Survey (eds. S. W. Hawking and W. Israel; Cambridge).

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  7. For classical and quantum description of homogeneous cosmologies, see M. Ryan, Hamiltonian Cosmology (Springer, 1972); M. A. H. MacCallum in General Relativity — An Einstein Survey (Cambridge, 1979); C. W. Misner in Magic without Magic (eds. J. Klauder; Freeman, 1972).

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  8. For detailed discussion of ‘minisuperspace’, see C. W. Misner, op. cit (ref. [7]) and B. S. De Witt (1967) Phys. Rev. 162, 1195.

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  9. This approach was initiated by J. V. Narlikar in (1979), M. N. Roy. Astron. Soc. 183, 159; Gen. Rel. Grav. (1979), 10, 883 and was developed further by the author; T. Padmanabhan (1982), PhD thesis.

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  10. It is easy to show that null geodesies remain null geodesies under conformal transformations, making the light cones conformally invariant. The converse is somewhat more difficult to prove but can be done.

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  11. Coordinate transformations expressing k = ± 1 FRW Universes in the conformally flat form are given in, e.g., F. Hoyle and J. V. Narlikar (1974) Action at a Distance in Physics and Cosmology (Freeman).

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  12. A down-to-earth discussion of path integrals can be found in R. P. Feynman and A. R. Gibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965). A flavour of more advanced topics can be found in L. S. Shulman, Techniques and Applications of Path Integration (Wiley, 1981).

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  13. For many of the details in this section and the next two, see J. V. Narlikar and T. Padmanabhan (1983) Phys. Repts. 100, 152 and T. Padmanabhan (1983) Phys. Rev. D28, 745.

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  14. An excellent discussion of this and related issues can be found in K. Kuchar, Canonical quantisation of gravity, in Relativity, Astrophysics and Cosmology (ed. W. Israel; Reidel, 1973); also see J. Hartle and K. Kuchar in Quantum Theory of Gravity, op. cit. (ref. [2]). The problem of separating temporal information from dynamical information is stressed in Kuchar’s article. For a more recent discussion, see T. Banks (1985), Nucl. Phys. B249, 332.

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  15. The ‘usual’ conclusion drawn is that “time is a semi-classical concept which cannot be extended... into the domain of quantum gravity”. See, e.g., T. Banks op. cit. [14], p. 336.

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  16. For previous discussion of this topic, see Hawking’s contribution in General Relativity — An Einstein Survey, op. cit. (e.g. ref. [6]).

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  17. This should be clear from the Schrödinger approach to field quantization described in Appendix 1. Also see J. Greensite and M. B. Halpern, Nucl. Phys. B242 (1984) 167.

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  18. This prescription is discussed for, e.g., in ref. [16].

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  19. The Wheeler-De Witt equation is discussed in many places. Particularly useful articles are the ones by Wheeler (1964; cited in ref. [2]), Kuchar (cited in ref. [14]) and D. R. Brill and R. H. Gowdy, Rep. Prog. Phys. (1970), 33, 413.

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  20. The role of observer in quantum cosmology is not clear. See, e.g., W. Patton and J. A. Wheeler in Quantum Gravity I, op. cit. (ref. [2]); T. Banks, op. cit. (ref. [14]).

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  23. See papers cited in ref. [13], and Phys. Letts. (1982), 87A, 226; (1983) 15, 435.

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  24. The comparison between the singular behaviour of hydrogen atom and the universe was first suggested by Wheeler. It is explored systematically in papers cited above (ref. [23]).

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  25. See, e.g., J. V. Narlikar (1979), M. N. Roy. Astron. Soc. 183, 159.

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  26. J. V. Narlikar (1984), Found. Phys. 14, 443; J. V. Narlikar (1981), Found. Phys., 11, 473; T. Padmanabhan and J. V. Narlikar (1982), Nature 295, 677.

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  27. See for, e.g., the papers in ref. [14].

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  28. The application of QSG is not limited to FRW models; for the application of QSG to other cases, see T. Padmanabhan (1982), Gen. Rel. Grav. 14, 549; Int. J. Theo. Phys. (1983), 22,1023 and Class. Q. Grav. (1984), 1, 149.

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  29. This semiclassical approximation is developed in T. Padmanabhan (1983), Phys. Rev. D28, 745; Detailed application to cosmology can be found in T. Padmanabhan (1983), Phys. Rev. D28, 756.

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  30. T. Padmanabhan (1983), Gen. Rel. Grav. 15, 435; Int. J. Theo. Phys. (1983), 22, 1023.

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  31. The analysis here is based on T. Padmanabhan (1983) Phys. Letts. 93A, 116. Creating the universe is a very popular pastime of quantum cosmologists, see, e.g., R. Brout et. al., Nucl. Phys. (1980), 170, 228; L. Lindley, Nature (1981), 291, 391; A. Vilenkin (1983), Phys. Rev. D27, 2848.

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  32. T. Padmanabhan (1984), Phys. Letts. 104A, 196.

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  33. This is similar to the vacuum functional in electromagnetism and is derived in T. Padmanabhan (1983) Phys. Letts. 96A, 110. For a detailed discussion of Equation (105), see Gen. Rel. Grav. (1985), 17, 215.

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  34. E.g., see B. De Witt, Phys. Rev. Letts. (1964), 13, 114; C. J. Isham, A. Salam, and J. Strathdee (1971), Phys. Rev. D3, 1805.

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  35. T. Padmanabhan (1985), Ann. Phys. 165, 38(1985); Current Science (1985), 54, 912.

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  36. J. Hartle and S. W. Hawking (1983), Phys. Rev. D28, 2960; S. W. Hawking (1984), Nucl. Phys. B239, 257.

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  37. For example, the ‘wave function of the inflationary Universe’ can be obtained as a E = 0 solution of GWD equation for the action in Equation (95). T. Padmanabhan (1985), TIFR preprint.

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  38. E. Baum, Phys. Letts. 133B (1983), 185.

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  1. Theoretical Astrophysics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India

    T. Padmanabhan

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B. R. Iyer N. Mukunda C. V. Vishveshwara

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© 1989 Kluwer Academic Publishers

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Padmanabhan, T. (1989). Quantum Cosmology — The Story So Far. In: Iyer, B.R., Mukunda, N., Vishveshwara, C.V. (eds) Gravitation, Gauge Theories and the Early Universe. Fundamental Theories of Physics, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2577-9_18

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  • DOI: https://doi.org/10.1007/978-94-009-2577-9_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7664-7

  • Online ISBN: 978-94-009-2577-9

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