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.Comment: Accepted for publication in Progress of Theoretical Physics, references added and typos corrected, 13 page

Scalar mode propagation in modified gravity with a scalar field

We study the propagation of the scalar modes around a Friedmann-Lemaitre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total four degrees of freedom. Two of these degrees will have a superluminal propagation--with k-dependent speed of propagation--whereas the other two will travel with the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depends on the second power of the modulus of the wave vector. Constraints are given and special cases are discussed.Comment: 13 pages, 1 figure, uses RevTe