Linear growth of matter density perturbations in f(R,G) theories

Abstract

We derive the equation of matter density perturbations on sub-horizon scales around a flat Friedmann-Lema\^ıtre-Robertson-Walker background for the general Lagrangian density $f(R,\GB)$ that is a function of a Ricci scalar $R$ and a Gauss-Bonnet term $\GB$. We find that the effective gravitational constant generically scales as distance squared at small distances. The effect of this diminishing of the gravitational constant might be important in the gravitational dynamics of cosmic objects such as galaxies, which can be in principle tested by observations. We also provide the general expressions for the effective anisotropic stress, which is useful to constrain modified gravity models from observations of large-scale structure and weak lensing. We also find that there is a special class of theories which evade this unusual behaviour and that the condition to belong to this special class is exactly the same as the one for not having super-luminal modes with propagation speed proportional to their wavenumber.

arXiv commentAccepted for publication in Progress of Theoretical Physics, references added and typos corrected, 13 pages

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• On the stability of the cosmological solutions in f(R,G) gravity
• A practical approach to cosmological perturbations in modified gravity
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Noether Symmetry Approach in Gauss-Bonnet Cosmology
• Regular black holes in $f(T)$ Gravity through a nonlinear electrodynamics source
• Locally Rotationally Symmetric Bianchi Type-I cosmological model in $f(T)$ gravity: from early to Dark Energy dominated universe
• Fab 5: Noncanonical Kinetic Gravity, Self Tuning, and Cosmic Acceleration
• Spherical Accretion of Matter by Charged Black Holes on f(T) Gravity
• Topological invariant quintessence
• Cosmological stability in $f(\varphi ,\mathcal{G})$ gravity
• Cosmological Tests of $f(R,G,T)$ Dark Energy Model in FRW Universe
• Constructions of $f(R,G,\mathcal{T})$ Gravity from Some Expansions of the Universe
• Reconstructing $f(T)$ modified gravity from ECHDE and ECNADE models
• The viable f(G) gravity models via reconstruction from the observations
• Purely metric Horndeski theories and spontaneous curvaturization of black holes
• Generalized Noether Theorem for Gauss-Bonnet Cosmology
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models