spot that eventually collapsed to form the Virgo supercluster and other familiar parts of our local universe. Cosmologists are used to thinking of looking out at the universe and measuring the prehistory of other regions of the universe. If we are fortunate enough to live in a compact hyperbolic universe, we can look out and see our own beginnings.

We thank Jeff Weeks and Bill Thurston for deepening our understanding of topology and for helpful comments. D.N.S. is supported by the MAP/MIDEX program. G.D.S. is supported through the National Science Foundation CAREER Grant. N.J.C was supported by Particle Physics and Astronomy Research Council Grant GR/L21488.

1. Strauss, M.A. & Willick, J.A. (1995) Phys. Rep. 261, 271–431.

2. Davis, M., Nusser, A. & Willick, J. (1996) Ap. J. 473, 22–41.

3. Riess, A.G., Davis, M., Baker, J. & Kirshner, R.P. (1997) Ap. J. 488, L1.

4. Bahcall, N.A., Lubin, L.M. & Dorman, V. (1995) Ap. J. 447, L81–L84.

5. White, S.D.M., Navarro, J.F., Evrard, A.E. & Frenk, C.S. (1993) Nature (London) 366, 429–433.

6. Lubin, L.M., Cen, R., Bahcall, N.A. & Ostriker, J.P. (1996) Ap. J. 460, L10–L13.

7. White, D.A., Jones, C. & Forman, W. (1997) Monogr. Nat. R. Astronom. Soc., in press.

8. Da Costa, L.N., Vogeley, M.S., Geller, M.J., Huchra, J.P. & Park, C. (1994) Ap. J. 437, L1–L4.

9. Lin, H., Kirshner, R.P., Shechtman, S.A., Landy, S.D., Oemler, A., Tucker, D. & Schechter, P.L. (1996) Ap. J. 471, 617–635.

10. Spergel, D.N., Bolte, M. & Freedman, W.L. (1997) Proc. Natl. Acad. Sci. USA 94, 6579–6584.

11. Carlberg, R.G., Yee, H.K.C., Ellingson, E., Morris, S.L., Abraham, R., Gravel, P., Hartwick, F.D.A., Hesser, J.E., Hutchings, J.B., Oke, J.B., Pritchet C.J. & Smecker-Hane, T. (1997) J.R. Assoc. Soc. Can. 90, 314–320.

12. Bahcall, N.A., Fan, X. & Cen, R. (1991) Ap. J. Lett. 485, L53–L56.

13. Kamionkowski, M. & Spergel, D.N. (1994) Ap. J. 432, 7–16.

14. Ratra, B., Sugiyama, N., Banday, A.J. & Gorski, K.M. (1991) Ap. J. 481, 22–34.

15. Ostriker, J.P. & Steinhardt, P.J. (1995) Nature (London) 377, 600–602.

16. Perlmutter, S., Gabi, S., Goldhaber, G., Goobar, A., Groom, D.E., et al. (1997) Ap. J. 483, 565–581.

17. Turner, E.L. (1990) Ap. J. 365, L43–L46.

18. Falco, E.E., Kochanek, C.S. & Munoz, J.M. (1997) Ap. J., in press.

19. Gott, J.R., III (1980) Monogr. Nat. R. Astronom. Soc. 193, 153–169.

20. Fagundes, H.V. (1983) Phys. Rev. Lett. 51, 517–520.

21. Cornish, N.J., Spergel, D.N. & Starkman, G.D. (1996) Phys. Rev. Lett. 77, 215–218.

22. Cornish, N.J., Spergel, D.N. & Starkman, G.D. (1996) astro-pk/9708225.

23. Bond, J.R., Pogosyan, D. & Souradeep, T. (1997) Proceedings of the 18th Texas Symposium on Relativistic Astrophysics, eds. Olinto, A., Frieman, J. & Schramm, D. (World Scientific, River Edge, NJ), in press.

24. Levin, J.J., Barrow, J.D., Bunn, E.F. & Silk, J. (1997) Phys. Rev. Lett., in press.

25. Weeks, J.R. (1985) The Shape of Space: How to Visualize Surfaces and Three Dimensional Manifolds (Dekker, New York).

26. Thurston, W.P. (1978) The Geometry and Topology of 3-Manifolds (Princeton Univ. Press, Princeton).

27. Balazs, N.L. & Voros, A. (1985) Phys. Rep. 143, 1109–1240.

28. Gutzweiler, M.C. Physica Scripta T9, 184–192.

29. Lehoucq, R., Lachieze-Rey, M. & Luminet, J.P. (1996) A & A 313, 339–346.

30. Roukema, B.F. & Edge, A.C. (1997) Monogr. Nat. R. Astonom. Soc., in press.



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement