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