- Access by Xinjiang University
Accelerating expansion or inhomogeneity? A comparison of the and Lemaître-Tolman models
Phys. Rev. D 89, 023520 – Published 30 January, 2014Erratum Phys. Rev. D 89, 089901 (2014)
DOI: https://doi.org/10.1103/PhysRevD.89.023520
Abstract
It is shown how certain observations interpreted in the background of the Friedmann model with (the model) can be reinterpreted using the Lemaître-Tolman (L-T) model so as to do away with the “dark energy.” The purpose of this paper is to clarify the underlying geometrical relations by doing the calculations as much as possible analytically or by very simple numerical programs. In the first part of the paper (fictitious) observations of the distribution of expansion velocity along the past light cone of the observer are considered. It is shown that the whole past light cone of the observer can be reproduced in the L-T model with . This is a geometric exercise that has the advantage of being free of numerical complications. In the second part, the luminosity distance-redshift relation of the model is duplicated using the L-T model with . The value of and the function are determined by the parameters. General properties of this L-T model are described. Difficulties of carrying the numerical calculations through the apparent horizon are presented in detail and mostly solved. The second model is a counterexample to the general belief that an L-T model mimicking must contain a void around the center—it has a peak of density at .
Erratum
See Also
Accelerating expansion or inhomogeneity? II. Mimicking acceleration with the energy function in the Lemaître-Tolman model
Blueshifts in the Lemaître-Tolman models
Article Text
References (47)
- S. Perlmutter et al., Astrophys. J. 517, 565 (1999).
- A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Krishner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, and J. Tonry, Astron. J. 116, 1009 (1998).
- Planck Collaboration, arXiv:1303.5076.
- G. Lemaître, Ann. Soc. Sci. Bruxelles A 53, 51 (1933); Gen. Relativ. Gravit. 29, 641 (1997).
- R. C. Tolman, Proc. Natl. Acad. Sci. U.S.A. 20, 169 (1934); Gen. Relativ. Gravit. 29, 935 (1997).
- M.-N. Célérier, Astron. Astrophys. 353, 63 (2000).
- H. Iguchi, T. Nakamura, and K. Nakao, Prog. Theor. Phys. 108, 809 (2002).
- M.-N. Célérier, K. Bolejko, and A. Krasiński, Astron. Astrophys. 518, A21 (2010).
- C. Quercellini, L. Amendola, A. Balbi, P. Cabella, and M. Quartin, Phys. Rep. 521, 95 (2012).
- R. A. Vanderveld, E. E. Flanagan, and I. Wasserman, Phys. Rev. D 74, 023506 (2006).
- A. Krasiński, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, England, 1997), pp. 317.
- J. Plebański and A. Krasiński, An Introduction to General Relativity and Cosmology (Cambridge University Press, Cambridge, England, 2006), pp. 534.
- C. Hellaby and K. Lake, Astrophys. J. 290, 381 (1985); 300, 461(E) (1986).
- H. Bondi, Mon. Not. R. Astron. Soc. 107, 410 (1947); Gen. Relativ. Gravit. 31, 1783 (1999).
- K. Bolejko, A. Krasiński, C. Hellaby, and M.-N. Célérier, Structures in the Universe by Exact Methods—Formation, Evolution, Interactions (Cambridge University Press, Cambridge, England, 2010), pp. 242.
- S. W. Hawking and G. F. R. Ellis, The Large-scale Structure of Spaceetime (Cambridge University Press, Cambridge, England, 1973).
- A. Krasiński and C. Hellaby, Phys. Rev. D 69, 043502 (2004).
- G. F. R. Ellis, in Proceedings of the International School of Physics ‘Enrico Fermi’, Course 47: General Relativity and Cosmology, ed. R. K. Sachs (Academic Press, New York, 1971), p. 104; Gen. Relativ. Gravit. 41, 581 (2009).
- W. Rindler, Mon. Not. R. Astron. Soc. 116, 662 (1956); Gen. Relativ. Gravit. 34, 133 (2002).
- A. Krasiński, C. Hellaby, K. Bolejko, and M.-N. Célérier, Gen. Relativ. Gravit. 42, 2453 (2010).
- A. Krasiński and K. Bolejko, Phys. Rev. D 83, 083503 (2011).
- A. Krasiński, Phys. Rev. D 84, 023510 (2011).
- A. Krasiński, Phys. Rev. D 86, 064001 (2012).
- P. Szekeres, in Gravitational Radiation, Collapsed Objects and Exact Solutions, edited by C. Edwards, Springer Lecture Notes in Physics (Springer, New York 1980), Vol. 124, p. 477.
- C. Hellaby and K. Lake, Astrophys. J. 282, 1 (1984); 294, 702(E) (1985).
- R. McMahon, Quasars and Galaxies at the Highest Redshifts. Crafoord Symposium 2005, http://powershow.com/view/24faaf-OTQ2Y/Quasars_and_Galaxies_at_the_Highest_Redshifts_powerpoint_ppt_presentation.
- M. Luciuk, Astronomical Redshift, http://www.asterism.org/tutorials/tut29-1.htm, last updated 2004.
- http://www.asknumbers.com/LengthConversion.aspx.
- M. L. McClure and C. Hellaby, Phys. Rev. D 78, 044005 (2008).
- J. Zibin, Phys. Rev. D 84, 123508 (2011); 78, 043504 (2008); also private communication from the anonymous referees of Ref. [8].
- A. Krasiński and C. Hellaby, Phys. Rev. D 69, 023502 (2004).
- P. Szekeres, Commun. Math. Phys. 41, 55, (1975).
- J. Silk, Astron. Astrophys. 59, 53 (1977).
- S. W. Goode and J. Wainwright, Phys. Rev. D 26, 3315, (1982).
- C. Clarkson and M. Regis, J. Cosmol. Astropart. Phys. 02 (2011) 013.
- K. Bolejko, M.-N. Célérier, and A. Krasiński, Classical Quantum Gravity 28, 164002 (2011).
- P. Bull, T. Clifton, and P. G. Ferreira, Phys. Rev. D 85, 024002 (2012).
- K. Bolejko, Phys. Rev. D 73, 123508 (2006).
- K. Bolejko, Phys. Rev. D 75, 043508 (2007).
- K. Bolejko, Gen. Relativ. Gravit. 41, 1585 (2009).
- K. Bolejko, Gen. Relativ. Gravit. 41, 1737 (2009).
- K. Bolejko, M.-N. Célérier, Phys. Rev. D 82, 103510 (2010).
- K. Bolejko and R. A. Sussman, Phys. Lett. B 697, 265 (2011).
- K. Bolejko, Astron. Astroph. 525, A49 (2011).
- K. Bolejko, C. Clarkson, R. Maartens, D. Bacon, N. Meures, and E. Beynon, Phys. Rev. Lett. 110, 021302 (2013).
- K. Bolejko, A. Krasiński, and C. Hellaby, Mon. Not. R. Astron. Soc. 362, 213 (2005).
- A. A. Friedmann, Z. Phys. 10, 377 (1922); Gen. Relativ. Gravit. 31, 1985 (1999); 32, 1937 (2000).