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The Early Universe and Observational Cosmology pp 169–189Cite as

Measuring Spacetime: From Big Bang to Black Holes

  • Part I The Very Early Universe and High Precision Cosmology
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Part of the book series: Lecture Notes in Physics ((LNP,volume 646))

Abstract

Space is not a boring static stage on which events unfold over time, but a dynamic entity with curvature, fluctuations and a rich life of its own which is a booming area of study. Spectacular new measurements of the cosmic microwave background, gravitational lensing, type Ia supernovae, large-scale structure, spectra of the Lyman α forest, stellar dynamics and x-ray binaries are probing the properties of spacetime over 22 orders of magnitude in scale. Current measurements are consistent with an infinite flat everlasting universe containing about 30% cold dark matter, 65% dark energy and at least two distinct populations of black holes.

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References

  • 1. A. Einstein: Relativity: the Special and the General Theory (Random House; New York, 1920)

    Google Scholar 

  • 2. S. Weinberg: Gravitation and Cosmology (Wiley, New York, 1972)

    Google Scholar 

  • 3. C. W. Misner, K. S. Thorne and J. A. Wheeler:Gravitation (Freeman, San Francisco, 1973).

    Google Scholar 

  • 4. The cosmic microwave background (CMB) is the oldest light around, emanating from the hot opaque hydrogen plasma that filled the universe during its first 400,000 years. An up-to-date review is: M. White and J. Cohn, 2002;astro-ph/0203120

    Google Scholar 

  • 5. The Lyman α forest (LyαF) is the plethora of absorption lines in the spectra of distant quasars caused by neutral hydrogen in overdense intergalactic gas along the line of sight. It allows us to map the cosmic gas distribution out to great distances.

    Google Scholar 

  • 6. http://map.gsfc.nasa.gov

    Google Scholar 

  • 7. http://www.mpa-garching.mpg.de/Virgo/

    Google Scholar 

  • 8. B. C. Bromley, W. A. Miller and V. I. Pariev: Nature;391, 54 (1998).

    Google Scholar 

  • 9. C. M. Will: Theory and Experiment in Gravitational Physics (Cambridge U. P., Cambridge, 1993)

    Google Scholar 

  • 10. G. F. Smoot et al: Astrophys. J. ; 396, L1 (1992)

    Google Scholar 

  • 11. M. Colless et al: Mon. Not. Roy. Astron. Soc., 328,1039 (2001).

    Google Scholar 

  • 12. I. Zehavi et al: Astrophys. J., 571, 172 (2002) [astro-ph/0106476].

    Google Scholar 

  • 13. F. Hoyle et al: Mon. Not. Roy. Astron. Soc. 329,336 (2002).

    Google Scholar 

  • 14. The CMB power spectrum is the level of temperature fluctuations as a function of angular scale, defined as the variance of the spherical harmonic coefficients of a sky map. A matter power spectrum is the level of 3D density fluctuations as a function of spatial scale, defined as the variance of the Fourier coefficients of the density field.

    Google Scholar 

  • 15. The measured power spectrum of galaxies or LyAF clouds may differ from the power spectrum that we really care about — that for the underlying dark matter. Bias is defined as the square root of the ratio of the two power spectra.

    Google Scholar 

  • 16. D. Scott, J. Silk and M. White: Science, 268, 829 (1995).

    Google Scholar 

  • 17. The CMB acronyms are the COsmic Background Explorer (COBE), Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics (BOOMERanG), Degree Angular Scale Interferometer (DASI) and Millimeter Anisotropy eXperiment IMaging Array (MAXIMA).

    Google Scholar 

  • 18. X. Wang, M. Tegmark and M. Zaldarriaga: Phys. Rev. D, 65, 123001 (2002) [astro-ph/0105091].

    Google Scholar 

  • 19. G. Efstathiou et al: Mon. Not. Roy. Astron. Soc.;330 L29 (2002) [astro-ph/0109152].

    Google Scholar 

  • 20. K. Schwarzschild: Vier. d. Astr. Ges. 35;337 (1900) English translation in Class. Quant. Grav. 15, 2539 (1998)

    Google Scholar 

  • 21. B. Roukema:2002;astro-ph/0201092

    Google Scholar 

  • 22. D. Stevens, D. Scott and J. Silk: Phys. Rev. Lett. 71, 20 (1993).

    Google Scholar 

  • 23. A. de Oliveira-Costa and G. F. Smoot: Astrophys. J. 448; 477 (1995).

    Google Scholar 

  • 24. A. de Oliveira-Costa, G. F. Smoot and A. A. Starobinski: Astrophys. J.;468;457(1996).

    Google Scholar 

  • 25. J. Levin: Phys. Rep. 365, 251 (2002) [gr-qc/0108043].

    Google Scholar 

  • 26. http://snap.lbl.gov

    Google Scholar 

  • 27. S. Perlmutter et al: Nature;391;51 (1998).

    Google Scholar 

  • 28. A. G. Riess et al: Astron. J.;116;1009 (1998).

    Google Scholar 

  • 29. P. M. Garnavich et al: Astrophys. J., 509, 74 (1998).

    Google Scholar 

  • 30. I. Maor, R. Brustein and P. Steinhardt Phys. Rev. Lett. 86, 6 (2001) [astro-ph/0007297].

    Google Scholar 

  • 31. D. Huterer and M. S. Turner: Phys. Rev. D 64, 123527 (2001) [astro-ph/0012510].

    Google Scholar 

  • 32. S. Burles, K. M. Nollett and M. S. Turner: Astrophys. J., 552, L1 (2001).

    Google Scholar 

  • 33. S. M. Carroll and M. Kaplinghat: Phys. Rev. D 65, 063507 (2002).

    Google Scholar 

  • 34. A. Guth and P. Steinhardt: Scientific American, May (1984).

    Google Scholar 

  • 35. A. D. Linde: Particle Physics and Inflationary Cosmology (Harwood, Chur, Switzerland 1990).

    Google Scholar 

  • 36. A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge U. P. Cambridge, UK, 2000).

    Google Scholar 

  • 37. J. Khoury et al: Phys. Rev. D;64;123522 (2001).

    Google Scholar 

  • 38. R. Kallosh, L. Kofman and A. D. Linde: Phys. Rev. D;64;123523 (2001).

    Google Scholar 

  • 39. P. J. Steinhardt and N. Turok: Science (2002).

    Google Scholar 

  • 40. J. B. Hartle and S. W. Hawking, Phys. Rev. D 28, 2960 (1983).

    Google Scholar 

  • 41. R. J. Gott and L. X. Li: Phys. Rev. D;58;023501 (1998).

    Google Scholar 

  • 42. G. Veneziano; 2000;hep-th/0002094

    Google Scholar 

  • 43. A. Vilenkin: Phys. Rev. Lett. 74, 846 (1995).

    Google Scholar 

  • 44. A. Loeb: Phys. Rev. D 65, 047301 (2002).

    Google Scholar 

  • 45. Y. Wang and P. M. Garnavich: Astrophys. J. 552, 445 (2001). [astro-ph/0101040].

    Google Scholar 

  • 46. M. Tegmark: Phys. Rev. D 66, 103507 (2002) [astro-ph/0101354].

    Google Scholar 

  • 47. M. Rowan-Robinson: The Cosmological Distance Ladder (Freeman, New York, 1985).

    Google Scholar 

  • 48. W. L. Freedman et al: Astrophys. J. 553, 47 (2001).

    Google Scholar 

  • 49. N. Bahcall et al: Science 284, 1481 (1999).

    Google Scholar 

  • 50. J. H. P. Wu: Phys. Rev. Lett. 87, 251303 (2001) [astro-ph/0104248].

    Google Scholar 

  • 51. O. Lahav et al;2001;astro-ph/0112162

    Google Scholar 

  • 52. R. A. C. Croft et al: Astrophys. J. 581, 20 (2002) [astro-ph/0012324].

    Google Scholar 

  • 53. S. Hannestad et al: Astropart. Phys. 17, 375 (2002) [astro-ph/0103047].

    Google Scholar 

  • 54. M. Bartelmann and P. Schneider: Phys. Rep. 340, 291 (2001).

    Google Scholar 

  • 55. D. M. Wittman et al: Nature, 405, 143 (2000).

    Google Scholar 

  • 56. L. Van Waerbeke et al;2000;A&A;358;30

    Google Scholar 

  • 57. D. J. Bacon, A. R. Refregier and R. S. Ellis: Mon. Not. Roy. Astron. Soc. 318, 625 (2000).

    Google Scholar 

  • 58. N. Kaiser, G. Wilson and G. A. Luppino ;2000;astro-ph/0003338

    Google Scholar 

  • 59. J. Rhodes, A. Refregier and E. J. Groth; 2001;astro-ph/0101213

    Google Scholar 

  • 60. L. Van Waerbeke et al;2001;astro-ph/0101511

    Google Scholar 

  • 61. R. H. Becker et al: Astron. J. 122, 2850 (2001).

    Google Scholar 

  • 62. S. G. Djorgovski: 2001;astro-ph/010806.

    Google Scholar 

  • 63. M. Tegmark and M. Zaldarriaga: Phys. Rev. D 66, 103508 (2002) [astro-ph/0207047].

    Google Scholar 

  • 64. M. Tegmark, A. J. S. Hamilton and Y. Xu: Mon. Not. Roy. Astron. Soc. 335, 887 (2002) [astro-ph/0111575].

    Google Scholar 

  • 65. H. Hoekstra, H. Yee and M. Gladders M: Astrophys. J. 577, 595 (2002) [astro-ph/0204295].

    Google Scholar 

  • 66. N. Y. Gnedin and A. J. S. Hamilton; 2001;astro-ph/0111194

    Google Scholar 

  • 67. I. Zehavi and A. Dekel: Nature, 401, 252 (1999).

    Google Scholar 

  • 68. N. A. Bahcall and X. Fan: Astrophys. J. 504, 1 (1998). [astro-ph/9803277].

    Google Scholar 

  • 69. E. Pierpaoli, D. Scott and M. White: Mon. Not. Roy. Astron. Soc. 325, 77 (2001) [astro-ph/0010039].

    Google Scholar 

  • 70. G. Holder, Z. Haiman and J. Mohr: 2001;astro-ph/0105396

    Google Scholar 

  • 71. P. McDonald et al: Astrophys. J. 543, 1 (2000).

    Google Scholar 

  • 72. M. Zaldarriaga, L. Hui, M. Tegmark: Astrophys. J. 557, 519 (2001) [astro-ph/0011559].

    Google Scholar 

  • 73. W. Hu, N. Sugiyama, J. Silk: Nature, 386, 37 (1997).

    Google Scholar 

  • 74. U. Seljak, M. Zaldarriaga: Astrophys. J. 469, 437 (1996).

    Google Scholar 

  • 75. W. Hu: Astrophys. J. 506, 485 (1998).

    Google Scholar 

  • 76. D. J. Eisenstein, W. Hu, M. Tegmark: Astrophys. J., 518, 2 (1999).

    Google Scholar 

  • 77. W. Hu et al: Phys. Rev. D 59, 023512 (1999).

    Google Scholar 

  • 78. L. Verde et al;2001;astro-ph/0112161

    Google Scholar 

  • 79. J. Wambsganss: 2000;astro-ph/0012423

    Google Scholar 

  • 80. A. Celotti, J. C. Miller, D. W. Sciama: Class. Quant. Grav. 16, A3 (2000).

    Google Scholar 

  • 81. J. H. Krolik : AGN : from the central black hole to the galactic environment (Princeton U. P. Princeton 1999).

    Google Scholar 

  • 82. J. Kormendy and K. Gebhardt;2001;astro-ph/0105230

    Google Scholar 

  • 83. A. Marconi: 2002;astro-ph/0201504

    Google Scholar 

  • 84. J. Frank, A. King, D. Raine: Accretion power in astrophysics, 3rd ed. (Cambridge U. P. Cambridge, 2002).

    Google Scholar 

  • 85. F. Zwicky: Helv. Phys. Acta, 6, 110 (1993).

    Google Scholar 

  • 86. H. Hoekstra et al: Astrophys. J. L. 548, L5 (2001).

    Google Scholar 

  • 87. N. Bahcall et al: Astrophys. J. 541, 1 (2000).

    Google Scholar 

  • 88. H. J. Newberg: Astrophys. J. 569, 245 (2002).

    Google Scholar 

  • 89. D. N. Spergel, P. J. Steinhardt: Phys. Rev. Lett. 84, 3760 (2000).

    Google Scholar 

  • 90. P. Bode, J. P. Ostriker, N. Turok: Astrophys. J. 556, 93 (2001) [astro-ph/0010389].

    Google Scholar 

  • 91. N. Dalal, C. S. Kochanek: 2002; astro-ph/0111456

    Google Scholar 

  • 92. A. Eckhardt et al;2002;astro-ph/0201031

    Google Scholar 

  • 93. F. Munyaneza, R. D. Viollier: Astrophys. J. 564, 274 (2002) [astro-ph/0103466].

    Google Scholar 

  • 94. K. Nandra: 2000;astro-ph/0007356

    Google Scholar 

  • 95. R. D. Blandford and R. L. Znajek: Mon. Not. Roy. Astron. Soc.,179, 433 (1997).

    Google Scholar 

  • 96. T. Shabhaz et al: Mon. Not. Roy. Astron. Soc., 271, L10 (1994).

    Google Scholar 

  • 97. E. Witten: Phys. Rev. D;30, 272 (1984).

    Google Scholar 

  • 98. S. Bahcall: Astrophys. J., 362, 251 (1990).

    Google Scholar 

  • 99. B. Carr: The Renaissance of GR and Cosmology, pp. 277. eds. G. F. R. Ellis et al (Cambridge U. P. Cambridge, 1993)

    Google Scholar 

  • 100. J. R. Oppenheimer and H. Snyder: Phys. Rev. 56, 455 (1939).

    Google Scholar 

  • 101. J. M. Miller: Astrophys. J. L. , 570, 69 (2002) [astro-ph/0202375].

    Google Scholar 

  • 102. I. H. Stairs et al: Astrophys. J. 505, 352 (1998).

    Google Scholar 

  • 103. S. A. Hughes et al;2001;astro-ph/0110349.

    Google Scholar 

  • 104. A. N. Lommen and D. C. Backer: Astrophys. J. 562, 297 (2001).[astro-ph/0107470].

    Google Scholar 

  • 105. M. Kamionkowski, A. Kosowsky, A. Stebbins: Phys. Rev. D, 55, 7368 (1997).

    Google Scholar 

  • 106. M. Zaldarriaga and U. Seljak: Phys. Rev. D, 55, 1830 (1997).

    Google Scholar 

  • 107. B. Boisseau et al: Phys. rev. Lett. 85, 2236 (2000).

    Google Scholar 

  • 108. M. Milgrom: Astrophys. J., 270, 365 (1983).

    Google Scholar 

  • 109. S. S. McGaugh: Astrophys. J.L 541, 33 (2000).

    Google Scholar 

  • 110. P. O. Mazur and E. Mottol: 2001;astro-ph/0103466

    Google Scholar 

  • 111. H. Yilmaz: Nuovo Cim. B, 107, 941 (1992).

    Google Scholar 

  • 112. C. W. Misner: Nuovo Cim. B, 114, 1079 (1999).

    Google Scholar 

  • 113. P. J. E. Peebles: Comments on the State of our Subject. In Clustering at High Redshift, Marseilles, June 1999, eds. A. Mazure and O. Le Fevre, [astro-ph/9910234].

    Google Scholar 

  • 114. J. A. Sellwood and A. Kosowsky: Does Dark Matter Exist?. In Gas & Galaxy Evolution eds. Hibbard, Rupen & van Gorkom ;2000;astro-ph/0009074

    Google Scholar 

  • 115. C. M. Will: The Confrontation between General Relativity and Experiment: A 1998 Update (Washington University, St. Louis), [gr-qc/9811036].

    Google Scholar 

  • 116. L. M. Griffiths, A. Melchiorri, J. Silk: Astrophys. J. 553, L5(2001)

    Google Scholar 

  • 117. M. White, D. Scott, E. Pierpaoli: Astrophys. J. 545, 1 (2000) [astro-ph/0004385].

    Google Scholar 

  • 118. M. White, C. S. Kochanek: Astrophys. J. 560, 539 (2001).

    Google Scholar 

  • 119. C. D. Hoyle et al: Phys. Rev. Lett. 86, 1418 (2001).

    Google Scholar 

  • 120. L. Randall: Science, 296, 1422 (2002).

    Google Scholar 

  • 121. The author wishes to thank Roger Blandford, Angélica de Oliveira-Costa and Harold Shapiro for helpful comments. Support for this work was provided by NSF grants AST-0071213 & AST-0134999, NASA grants NAG5-9194 & NAG5-11099, and the David and Lucile Packard Foundation.

    Google Scholar 

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  1. Dept. of Physics, Univ. of Pennsylvania, Philadelphia, PA 19104,  

    Max Tegmark

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  1. Max Tegmark
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Nora Bretón Jorge Luis Cervantes-Cota Marcelo Salgado

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Tegmark, M. Measuring Spacetime: From Big Bang to Black Holes. In: Bretón, N., Cervantes-Cota, J.L., Salgado, M. (eds) The Early Universe and Observational Cosmology. Lecture Notes in Physics, vol 646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40918-2_6

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