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The Evolution of density perturbationsin modified theories of gravity

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart  and
P. Dunsby
P. Dunsby*
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa
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Abstract

We present the Covariant and Gauge Invariant theory of scalar perturbations of a Friedmann-Lemaître-Robertson-Walker universe for Fourth Order Gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbation equations are applied to a simple background solution of Rn gravity and we obtain exact solutions of the perturbation equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular we find that for all values of n there is always a growing mode for the density contrast, even if the universe is in a state of accelerated expansion. Such a behavior does not occur in standard General Relativity, where as soon as Dark Energy dominates, the density contrast experiences an unrelenting decay. Consequently, this peculiarity in the framework of higher order gravity model is sufficently novel to warrant further investigation.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles, ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 141 - 147
Copyright
© EAS, EDP Sciences, 2008

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References

Ananda, K., Carloni, S., & Dunsby, P.K.S., 2007
Bardeen, J.M., 1980, Phys. Rev. D, 22, 1982 CrossRef
Bean, R., Bernat, D., Pogosian, L., Silvestri, A., & Trodden, M., 2007, Phys. Rev. D, 75, 064020 [arXiv:astro-ph/0611321] CrossRef
Bruni, M., Dunsby, P.K.S., & Ellis, G.F.R., 1992, ApJ, 395, 34 CrossRef
Bruni, M., Ellis, G.F.R., & Dunsby, P.K.S., 1992, Class. Quant. Grav., 9, 921 CrossRef
Carloni, S., Dunsby, P., & Troisi, A., 2008, Phys. Rev. D, 77, 024024 CrossRef
Carloni, S., Dunsby, P., Capozziello, S., & Troisi, A., 2005, Class. Quant. Grav. 22, 4839
Carloni, S., Leach, J.A., Capozziello, S., & Dunsby, P.K.S. [arXiv:gr-qc/0701009]
Carloni, S., Troisi, A., & Dunsby, P.K.S., Some remarks on the dynamical systems approach to fourth order gravity [arXiv:0706.0452] [gr-qc] submitted to CQG
Chavel, I., 1994, Riemannian Geometry: A Modern Introduction (New York: Cambridge University Press)
Dunsby, P.K.S., Bruni, M., & Ellis, G.F.R., 1992, A&A, 395, 54
Dunsby, P.K.S., Bassett, B.A.C., & Ellis, G.F.R., 1997, Class. Quant. Grav., 14, 1215 [arXiv:gr-qc/9811092] CrossRef
Dunsby, P.K.S., & Bruni, M., 1994, Int. J. Mod. Phys. D, 3, 443 [arXiv:gr-qc/9405008] CrossRef
Dunsby, P.K.S., Carloni, S., & Ananda, K., 2008, in preparation
Eddington, A.S., 1952, The mathematical theory of relativity (Cambridge: Cambridge Univ. Press)
Ellis, G.F.R., & Bruni, M., 1989, Phys. Rev. D, 40, 1804 CrossRef
Ellis, G.F.R., Bruni, M., & Hwang, J., 1990, Phys. Rev. D, 42, 1035 CrossRef
Ellis, G.F.R., & van Elst, H., Cosmological Models, Cargèse Lectures 1998, 1999, in Theoretical and Observational Cosmology, Ed. M Lachièze-Rey (Dordrecht: Kluwer), 1 [arXiv:gr-qc/9812046]
Hawking, S.W., & Ellis, G.F.R., 1973, The Large scale structure of space-time (Cambridge University Press, Cambridge)
Kodama, H., & Sasaki, M., 1984,Prog. Theor. Phys. Suppl., 78, 1
Maarteens, R., & Taylor, D.R., 1994, Gen. Relativ. Grav. , 26, 599 CrossRef
Stewart, J.M., 1990, Perturbations of Friedmann - Robertson - Walker cosmological models, Class. Quant. Grav., 7, 1169 CrossRef