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References

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    S. MacDowell, and F. Mansouri, Phys. Rev. Lett. 739, 1376 (1977).
  • 2
    L. Freidel, and A. Starodubtsev, arXiv 0501191
  • 3
    For general-relativity cognos-centi, there exists a generalized definition of this boundary region. On the dark-energy side, the Riemann curvature tensor, expressed in 6 x 6 Petrov matrix form, is to good approximation a multiple of the unit matrix. On the matter side, it differs greatly and typically has both positive and negative eigenvalues. Note that this way of expressing the criterion is local, as well as general-covariant.
  • 4
    D. Kaplan, A. Nelson, and N. Weiner, Phys. Rev. Lett. 93, 091801 (2004). (arXiv 0401099)
  • 5
    We follow here, more or less, the Freidel-Starodubtsev description [2].
  • 6
    Y. Zeldovich, JETP Lett. 6, 316 (1967).
  • 7
    S. Carniero, arXiv 0305081; R. Schutzhold, arXiv 0204018; A. Randono, arXiv 0805.2955; N. Poplawski, arXiv 1005.0893; F. Urban and A. Zhitnitsky, arXiv 0906.2162, 0906.2165, and 0909.2684
  • 8
    R. Kolb, and M. Turner, The Early Universe (Westview Press, 1994), p. 65.
  • 9
    A lucid introduction to this metric description is given in U. Fischer, and M. Visser, Ann. Phys. (New York) 304, 22 (2003) (arXiv 0205139).
  • 10
    E. Verlinde, JHEP04 029, (2011), (arXiv 1001.0783).
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    T. Jacobson, Phys. Rev. Letts. 75, 1260 (1995); T. Padmanabhan, arXiv 0911.5004 and references therein; W. Unruh, Phys. Rev. D 14, 870 (1976).
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    G. Volovik, The Universe in a Helium Droplet (Oxford U. Press, USA, 2003).
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    J. Gasser, and H. Leutwyler, Ann. Phys.(New York) 158, 142 (1984); see also S. Scheer, arXiv 0908.3425.
  • 14
    See for example G. Trayling, arXiv 9912231; A.G. Lisi, arXiv 0711.0770; F. Nesti and R. Percacci, arXiv 0909.4537.
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    R. Buniy and T. Kephart, Phys. Lett. A 373, 919 (2009) (arXiv 0808.1891).
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    M. Baker, H.M. Chan, and S.T. Tsou, arXiv 1206.0199 and references therein.
  • 17
    Fig 3. of M. Baker, J. Bordes, H.M. Chan, and S.T. Tsou, arXiv 1103.5615, fits my expression very well.
  • 18
    See for example R. Essig, J. Mardon, and T. Volonsky, Phys. Rev. D 85, 076007 (2012) (arXiv 1108.5385).
  • 19
    This feature seems to be undervalued by the general-relativity community. See however, e.g. A. Randono and S. Mercuri, Class. Quant. Grav. 28, 025001 (2011) (arXiv 1005.1291) and references therein; see also [2].
  • 20
    S. Holst, Phys. Rev. D 53, 5966 (1996), (arXiv 9511026).
  • 21
    See, for example, F. Hehl, arXiv 1204.3672 and references therein.
  • 22
    See, for example, J. Bjorken, arXiv 1008.0033; see also [2].
  • 23
    R. Peccei, arXiv 0607268 and references therein.
  • 24
    The underlying mathematical foundation is the Erlangen Program for geometry, initiated by Felix Klein. The fundamentals are clearly elucidated by D. Wise, arXiv 1112.2390; also Class. Quant. Gravity 27, 155010 (2010) (arXiv 0611154). I highly recommend these very interesting papers.