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

Understand

We derive the equation of matter density perturbations on sub-horizon scales around a flat Friedmann-Lema\^\i tre-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.