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Averaging in cosmology
Phys. Rev. D 57, 798 – Published 15 January, 1998
DOI: https://doi.org/10.1103/PhysRevD.57.798
Abstract
In this paper we discuss the effect of local inhomogeneities on the global expansion of nearly Friedmann-Lemaitre-Robertson-Walker (FLRW) universes, in a perturbative setting. We derive a generic linearized averaging operation for metric perturbations from basic assumptions, and we explicate the issue of gauge invariance. We derive a gauge invariant expression for the back reaction of density inhomogeneities on the global expansion of perturbed FLRW spacetimes, in terms of observable quantities, and we calculate the effect quantitatively. Since we do not adopt a comoving gauge, our result incorporates the back reaction on the metric due to scalar velocity and vorticity perturbations. The results are compared with the results by other authors in this field.
References (21)
- T. Futamase, Phys. Rev. D 53, 681 (1996).
- S. Bildhauer and T. Futamase, Gen. Relativ. Gravit. 23, 1251 (1991).
- R. M. Zalaletdinov, Gen. Relativ. Gravit. 24, 1015 (1992).
- R. M. Zalaletdinov, Gen. Relativ. Gravit. 25, 673 (1993).
- M. Carfora and A. Marzuoli, Phys. Rev. Lett. 53, 2445 (1984).
- J. M. Bardeen, Phys. Rev. D 22, 1882 (1980).
- C. C. Dyer and R. C. Roeder, Astrophys. J. 172, L115 (1972).
- G. F. R. Ellis, General Relativity and Gravitation, edited by B. Bertotti et al. (Reidel, Dordrecht, 1984), pp. 215–288.
- G. ’t Hooft and M. Veltman, Ann. Inst. Henri Poincaré 20, 69 (1974).
- M. Bruni et al., Class. Quantum Grav. 14, 2585 (1997).
- D. M. Eardley and L. Smarr, Phys. Rev. D 19, 2239 (1979).
- P. J. E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, NJ, 1993), p. 508.
- P. Coles and F. Lucchin, The Origin and Evolution of Cosmic Structure (Wiley, New York, 1995), p. 265.
- C. B. Collins and S. W. Hawking, Mon. Not. R. Astron. Soc. 162, 307 (1973).
- C. B. Collins and G. F. R. Ellis, Phys. Rep. 56, 65 (1979).
- C. G. Hewitt et al., in Dynamical Systems in Cosmology, edited by J. Wainwright and G. F. R. Ellis (Cambridge University Press, Cambridge, England, 1997), Chap. 9.
- M. Clutton-Brock and P. J. E. Peebles, Astron. J. 86, 1115 (1981).
- M. Davis and P. J. E. Peebles, Astrophys. J. 267, 465 (1983).
- R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984), p. 437.
- T. Buchert and J. Ehlers, Astron. Astrophys. 320, 1 (1997).
- H. Russ et al., Phys. Rev. D 53, 6881 (1996).