Energy conditions in the epoch of galaxy formation

Science

Volumn 276, Issue 5309, 1997, Pages 88-90

  Visser, Matt ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ASTRONOMY; COSMOS; DENSITY; ENERGY; MATHEMATICAL MODEL; PRIORITY JOURNAL;

EID: 0030894093     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.276.5309.88     Document Type: Article

References (37)

1. S. W. Hawking and G. F. R. Ellis, The Large-Scale Structure of Space-Time (Cambridge Univ. Press, Cambridge, 1973), pp. 88-91 and pp. 95-96.
2. R. M. Wald, General Relativity (Univ. of Chicago Press, Chicago, IL, 1984), pp. 218-220.
3. M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 115-118.
4. S. W. Hawking and G. F. R. Ellis, The Large-Scale Structure of Space-Time (Cambridge Univ. Press, Cambridge, 1973), pp. 263, 266, 271, 272, 292-293, 311, 318, 320, and 354-357.
5. R. M. Wald, General Relativity (Univ. of Chicago Press, Chicago, IL, 1984), pp. 226-227, 232, 233, and 237-241.
6. M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 118-119.
7. 4 [M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 128-129]. Here ℏ is Planck's constant, c is the speed of light, G is Newton's constant, and M is the mass of the body under consideration. These quantum effects are not expected to be significant for large classical systems, particularly in cosmological settings. For a general discussion of quantum effects in semiclassical gravity, see N. D. Birrell and P. C. W. Davies, [Quantum Fields in Curved Spacetime (Cambridge Univ. Press, Cambridge, 1982)] and S. A. Fulling, [Aspects of Quantum Field Theory in Curved Space-Time (Cambridge Univ. Press, Cambridge, 1989)].
8. 4 [M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 128-129]. Here ℏ is Planck's constant, c is the speed of light, G is Newton's constant, and M is the mass of the body under consideration. These quantum effects are not expected to be significant for large classical systems, particularly in cosmological settings. For a general discussion of quantum effects in semiclassical gravity, see N. D. Birrell and P. C. W. Davies, [Quantum Fields in Curved Spacetime (Cambridge Univ. Press, Cambridge, 1982)] and S. A. Fulling, [Aspects of Quantum Field Theory in Curved Space-Time (Cambridge Univ. Press, Cambridge, 1989)].
9. 4 [M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 128-129]. Here ℏ is Planck's constant, c is the speed of light, G is Newton's constant, and M is the mass of the body under consideration. These quantum effects are not expected to be significant for large classical systems, particularly in cosmological settings. For a general discussion of quantum effects in semiclassical gravity, see N. D. Birrell and P. C. W. Davies, [Quantum Fields in Curved Spacetime (Cambridge Univ. Press, Cambridge, 1982)] and S. A. Fulling, [Aspects of Quantum Field Theory in Curved Space-Time (Cambridge Univ. Press, Cambridge, 1989)].
10. General Relativity: An Einstein Centenary Survey, S. W. Hawking and W. Israel, Eds. (Cambridge Univ. Press, Cambridge, 1979).
11. Three Hundred Years of Gravitation, S. W. Hawking and W. Israel, Eds. (Cambridge Univ. Press, Cambridge, 1987).
12. M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 53-73.
13. Look-back time to an object is simply defined as the difference between the age of the universe now and the age of the universe when the light that we are now receiving from that object was emitted.
14. Cosmological inflation is a brief period of anomalously rapid expansion in the early universe during which the universe inflates by an enormous factor. Inflation is commonly invoked as a hypothesis to explain the horizon problem, the flatness problem, and the monopole problem, as discussed in (13-15).
15. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Redwood City, CA, 1990).
16. A. D. Linde, Inflation and Quantum Cosmology (Academic Press, Boston, MA, 1990).
17. I. Moss, Quantum Theory, Black Holes, and Inflation (Wiley, Chichester, UK, 1996).
18. S. Leonard and K. Lake, Astrophys. J. 441, L55 (1995).
19. P. J. E. Peebles, Principles of Physical Cosmology (Princeton Univ. Press, Princeton, NJ, 1993).
20. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), pp. 412-415.
21. A cosmological constant, if present, is absorbed into the definition of the total density and total pressure.
22. Negative energy densities are extremely rare in physics. The only known examples are from small quantum effects [such as the experimentally verified Casimir effect; see M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 121-125] or from a hypothetical negative cosmological constant (see M. Visser, ibid., pp. 129-130). Negative energy does not mean antimatter. Antimatter has positive energy. Negative energy means an energy less than that of the normal undisturbed vacuum.
23. Negative energy densities are extremely rare in physics. The only known examples are from small quantum effects [such as the experimentally verified Casimir effect; see M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), pp. 121-125] or from a hypothetical negative cosmological constant (see M. Visser, ibid., pp. 129-130). Negative energy does not mean antimatter. Antimatter has positive energy. Negative energy means an energy less than that of the normal undisturbed vacuum.
24. A standard candle is any class of astrophysical objects that is sufficiently well understood, sufficiently well characterized, and has sufficiently nice observational features to be widely accepted by observational astronomers as a useful diagnostic tool. The most famous standard candles are the Cephid variables, whose absolute luminosity is a known function of their period [P. J. Peebles, in (17), pp. 20 and 106, and S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), pp. 433-438]. Here I want a similarly well-behaved class of objects in order to trace out galaxy formation.
25. A standard candle is any class of astrophysical objects that is sufficiently well understood, sufficiently well characterized, and has sufficiently nice observational features to be widely accepted by observational astronomers as a useful diagnostic tool. The most famous standard candles are the Cephid variables, whose absolute luminosity is a known function of their period [P. J. Peebles, in (17), pp. 20 and 106, and S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), pp. 433-438]. Here I want a similarly well-behaved class of objects in order to trace out galaxy formation.
26. P. J. E. Peebles, in (17), p. 106.
27. 16 m.
28. P. J. E. Peebles, in (17), pp. 610-611. Note the large uncertainties.
29. f.
30. Particle Data Group, Review of Particle Properties, Phys. Rev. D54 (1996). See the mini-review on pp. 112-114 and references therein. Slightly different numbers are given on p. 66.
31. The standard picture is that the universe is matter-dominated (by dust) out to z ≈ 1000, so that one expects the equation of state to be p = O. P. J. E. Peebles, in (17), p. 100.
32. P. J. E. Peebles, in (17), pp. 106-108.
33. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), pp. 441-451.
34. S. W. Hawking and G. F. R. Ellis, The Large-Scale Structure of Space-Time (Cambridge Univ. Press, Cambridge, 1973), p. 95.
35. M. Visser, Lorentzian Wormholes - from Einstein to Hawking (AIP Press, New York, 1995), p. 120.
36. 27 K, whereas galaxy formation takes place for T ≤ 60 K.
37. Supported by the U.S. Department of Energy.