Dispersion of growth of matter perturbations in f(R) gravity

Shinji Tsujikawa*, Radouane Gannouji, Bruno Moraes, David Polarski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

111 Citations (Scopus)


We study the growth of matter density perturbations δm for a number of viable f(R) gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density f is a function of the Ricci scalar R. If the parameter m ≡ Rf,RR/f,R today is larger than the order of 10-6, linear perturbations relevant to the matter power spectrum evolve with a growth rate s ≡ d ln □ δm/d ln □ a (a is the scale factor) that is larger than in the ΛCDM model. We find the window in the free parameter space of our models for which spatial dispersion of the growth index γ0 ≡ γ(z=0) (z is the redshift) appears in the range of values 0.40 □ γ0 0.55, as well as the region in parameter space for which there is essentially no dispersion and γ0 converges to values around 0.40 □ γ □ 0.43. These latter values are much lower than in the ΛCDM model. We show that these unusual dispersed or converged spectra are present in most of the viable f(R) models with m(z=0) larger than the order of 10-6. These properties will be essential in the quest for f(R) modified gravity models using future high-precision observations and they confirm the possibility to distinguish clearly most of these models from the ΛCDM model.

Original languageEnglish
Article number084044
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number8
Publication statusPublished - 2009 Oct 29
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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