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Prologue: Inside the Energy Walls of Our “Cradle”

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Abstract

We often say that the physics of “small distances” is equivalent to the physics of “high energies.” This is indeed true, as a direct consequence of the celebrated Heisenberg’s principle (or uncertainty principle) stating that, in order to explore (and measure) smaller and smaller distances, we need probes with higher and higher momenta, namely with larger and larger kinetic energies. According to the uncertainty principle, in particular, the required energy E turns out to be inversely proportional to the considered distance d, so that E tends to infinity when the distance d goes to zero.

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Notes

  1. 1.

    The famous Andromeda Galaxy, whose picture is also used as a desktop background in recent versions of Mac computers, is one of the nearest galaxies, and is approximately 2.5 million light-years away from Earth (corresponding to a distance of about 2. 4 × 1019 km).

  2. 2.

    This occurs when the radiation reaches a temperature that is about a 1,000 times larger than the current one: more precisely, a temperature of 2,973 K. Such a temperature is reached at the so-called “decoupling epoch,” see for instance the textbooks by Durrer [1], Weinberg [2], Gasperini [3] (in Italian).

References

  1. R. Durrer, The Cosmic Microwave Background (Cambridge University Press, Cambridge, 2008)

    Book  Google Scholar 

  2. S. Weinberg, Cosmology (Oxford University Press, Oxford, 2008)

    MATH  Google Scholar 

  3. M. Gasperini, Lezioni di Cosmologia Teorica (Spriger, Milano, 2012)

    Book  MATH  Google Scholar 

  4. E.G. Adelberger, B.R. Heckel, A.E. Nelson, Ann. Rev. Nucl. Part. Sci. 53, 77 (2003)

    Article  ADS  Google Scholar 

  5. E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, S.H. Aronson, Phys. Rev. Lett. 56, 3 (1986)

    Article  ADS  Google Scholar 

  6. R. Barbieri, S. Cecotti, Z. Phys. C 33, 255 (1986)

    Google Scholar 

  7. M. Gasperini, Phys. Rev. D 40, 325 (1989)

    Google Scholar 

  8. M. Gasperini, Phys. Rev. D 63, 047301 (2001)

    Google Scholar 

  9. T. Taylor, G. Veneziano, Phys. Lett. B 213, 459 (1988)

    Google Scholar 

  10. M. Gasperini, Phys. Lett. B 327, 314 (1994); M. Gasperini, G. Veneziano, Phys. Rev. D 50, 2519 (1994)

    Google Scholar 

  11. J. Khoury, A. Weltman, Phys. Rev. D 69, 044026 (2004)

    Google Scholar 

  12. R. Sundrum, Phys. Rev. D 69, 044014 (2004)

    Google Scholar 

  13. T. Kaluza, Sitzungsber. Preuss. Akad. Wiss. Berlin 1921, 966 (1921); O. Klein, Z. Phys. 37, 895 (1926)

    Google Scholar 

  14. N. Arkani Hamed, S. Dimopoulos, G.R. Dvali, Phys. Lett. B 429, 263 (1998)

    Google Scholar 

  15. I. Antoniadis, Phys. Lett. B 246, 377 (1990)

    Google Scholar 

  16. L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4960 (1999)

    Google Scholar 

  17. A.G. Riess et al., Astron. J. 116, 1009 (1998); S. Perlmutter et al., Astrophys. J 517, 565 (1999)

    Google Scholar 

  18. G. Dvali, G. Gabadadze, M. Porrati, Phys. Lett. B 485, 208 (2000)

    Google Scholar 

  19. I. Slatev, L. Wang, P.J. Steinhardt, Phys. Rev. Lett. 82, 869 (1999)

    Google Scholar 

  20. C. Armendariz-Picon, V. Mukhanov, P.J. Steinhardt, Phys. Rev. Lett. 85, 4438 (2000)

    Article  ADS  Google Scholar 

  21. M. Gasperini, Phys. Rev. D 64, 043510 (2001)

    Google Scholar 

  22. M. Gasperini, F. Piazza, G. Veneziano, Phys. Rev. D 65, 023508 (2001)

    Google Scholar 

  23. L. Amendola, M. Gasperini, F. Piazza, JCAP 09, 014 (2004); Phys. Rev. D 4, 127302 (2006)

    Google Scholar 

  24. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. B. Zumino, Nucl. Phys. B 89, 535 (1975)

    Google Scholar 

  26. E. Witten, in Sources and Detection of Dark Matter and Dark Energy in the Universe, ed. by D.B. Cline (Springer, Berlin, 2001), p. 27

    Chapter  Google Scholar 

  27. R. Bousso, Gen. Rel. Grav. 40, 607 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. T. Padmanabhan, Gen. Rel. Grav. 40, 529 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  29. A. Kobakhidze, N.L. Rodd, Int. J. Theor. Phys. 52, 2636 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  30. M. Gasperini, JHEP 06, 009 (2008)

    Article  ADS  Google Scholar 

  31. I. Antoniadis, E. Dudas, A. Sagnotti, Phys. Lett. B 464, 38 (1999)

    Google Scholar 

  32. G.F.R. Ellis, Spacetime and the Passage of Time, arXiv:1208.2611, published in “Springer Hanbook of Spacetime”, ed. by A. Ashtekar, V. Petkov (Springer, Berlin, 2014)

    Google Scholar 

  33. P.C.W. Davies, Sci. Am. (Special Edition) 21, 8 (2012)

    Google Scholar 

  34. J.B. Barbour, The End of Time: The Next Revolution in Physics (Oxford University Press, Oxford, 1999)

    Google Scholar 

  35. J.D. Barrow, D.J. Shaw, Phys. Rev. Lett. 106, 101302 (2011)

    Article  ADS  Google Scholar 

  36. N. Kaloper, K.A. Olive, Phys. Rev. D 57, 811 (1998)

    Google Scholar 

  37. E. Caianiello, La Rivista del Nuovo Cimento 15, 1 (1992)

    Article  Google Scholar 

  38. M. Gasperini, Int. J. Mod. Phys. D 13, 2267 (2004)

    Google Scholar 

  39. B. Zwiebach, A First Course in String Theory (Cambridge University Press, Cambridge, 2009)

    Book  MATH  Google Scholar 

  40. M.B. Green, J. Schwartz, E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987)

    MATH  Google Scholar 

  41. J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998)

    Book  Google Scholar 

  42. M. Gasperini, Elements of String Cosmology (Cambridge University Press, Cambridge, 2007)

    Book  MATH  Google Scholar 

  43. M.A. Virasoro, Phys. Rev. D 1, 2933 (1970)

    Google Scholar 

  44. P. Ramond, Phys. Rev. D 3, 2415 (1971)

    Google Scholar 

  45. A. Neveau, J.H. Schwarz, Nucl. Phys. B 31, 86 (1971)

    Google Scholar 

  46. F. Gliozzi, J. Scherk, A. Olive, Nucl. Phys. B 122, 253 (1977)

    Google Scholar 

  47. A. Sagnotti, J. Phys. A 46, 214006 (2013)

    Google Scholar 

  48. K. Kikkawa, M.Y. Yamasaki, Phys. Lett. B 149, 357 (1984)

    Google Scholar 

  49. N. Sakai, I. Senda, Prog. Theor. Phys. 75, 692 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  50. A.A. Tseytlin, Mod. Phys. Lett. A 6, 1721 (1991)

    Google Scholar 

  51. G. Veneziano, Phys. Lett. B 265, 287 (1991)

    Google Scholar 

  52. E. Witten, Nucl. Phys. B 443, 85 (1995)

    Google Scholar 

  53. R. Bousso, J. Polchinski, Sci. Am. 291, 60 (2004)

    Article  Google Scholar 

  54. R. Brandenberger, C. Vafa, Nucl. Phys. B 316, 391 (1989)

    Google Scholar 

  55. A.A. Tseytlin, C. Vafa, Nucl. Phys. B 372, 443 (1992)

    Google Scholar 

  56. S. Alexander, R. Brandenberger, D. Easson, Phys. Rev. D 62, 103509 (2000)

    Google Scholar 

  57. S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972)

    Google Scholar 

  58. A.A. Penzias, R.W. Wilson, Astrophys. J. 142, 419 (1965)

    Article  ADS  Google Scholar 

  59. J. Smooth et al., Astrophys. J. 396, L1 (1992)

    Article  ADS  Google Scholar 

  60. A. Guth, Phys. Rev. D 23, 347 (1981)

    Google Scholar 

  61. E.W. Kolb, M.S. Turner, The Early Universe (Addison Wesley, Redwood City, 1990)

    MATH  Google Scholar 

  62. A. Borde, A. Guth, A. Vilenkin, Phys. Rev. Lett. 90, 151301 (2003)

    Article  ADS  Google Scholar 

  63. M. Gasperini, G. Veneziano, Astropart. Phys. 1, 317 (1993); Phys. Rep. 373, 1 (2003)

    Google Scholar 

  64. M. Gasperini, The Universe Before the Big Bang: Cosmology and String Theory (Springer, Berlin, 2008)

    Google Scholar 

  65. J. Khoury, B.A. Ovrut, P.J. Steinhardt, N. Turok, Phys. Rev. D 64, 123522 (2001)

    Google Scholar 

  66. P.J. Steinhardt, N. Turok, Phys. Rev. D 65, 126003 (2002)

    Google Scholar 

  67. N. Goheer, M. Kleban, L. Susskind, JHEP 0307, 056 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  68. C. Burgess et al., JHEP 0107, 047 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  69. S. Kachru et al., JCAP 0310, 013 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  70. R. Penrose, Cycles of Time: An Extraordinary New View of the Universe (Bodley Head, London, 2010)

    Google Scholar 

  71. V.G. Gurzadyan, R. Penrose, Eur. Phys. J. Plus 128, 22 (2013)

    Article  Google Scholar 

  72. M. Gasperini, M. Giovannini, Phys. Lett. B 282, 36 (1992); Phys. Rev. D 47, 1519 (1993)

    Google Scholar 

  73. R. Brustein, M. Gasperini, G. Venenziano, Phys. Lett. B 361, 45 (1995)

    Google Scholar 

  74. M. Maggiore, Gravitational Waves (Oxford University Press, Oxford, 2007)

    Book  Google Scholar 

Download references

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Gasperini, M. (2014). Prologue: Inside the Energy Walls of Our “Cradle”. In: Gravity, Strings and Particles. Springer, Cham. https://doi.org/10.1007/978-3-319-00599-7_1

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