Second-order matter density perturbations and skewness in scalar-tensor modified gravity models

Takayuki Tatekawa*, Shinji Tsujikawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We study second-order cosmological perturbations in scalar-tensor models of dark energy that satisfy local gravity constraints, including f(R) gravity. We derive equations for matter fluctuations under a sub-horizon approximation and clarify conditions under which first-order perturbations in the scalar field can be neglected relative to second-order matter and velocity perturbations. We also compute the skewness of the matter density distribution and find that the difference from the ΛCDM (CDM: cold dark matter) model is less than a few per cent even if the growth rate of first-order perturbations is significantly different from that in the ΛCDM model. This shows that the skewness provides a model-independent test for the picture of gravitational instability from Gaussian initial perturbations including scalar-tensor modified gravity models.

Original languageEnglish
Article number009
JournalJournal of Cosmology and Astroparticle Physics
Issue number9
Publication statusPublished - 2008 Sept 1
Externally publishedYes


  • Cosmological perturbation theory
  • Dark energy theory

ASJC Scopus subject areas

  • Astronomy and Astrophysics


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