Cosmological perturbation in f(R,G) theories with a perfect fluid

Understand

In order to classify modified gravity models according to their physical properties, we analyze the cosmological linear perturbations for f(R,G) theories (R being the Ricci scalar and G, the Gauss-Bonnet term) with a minimally coupled perfect fluid.

• For the scalar type perturbations, we identify in general six degrees of freedom.
• We find that two of these physical modes obey the same dispersion relation as the one for a non-relativistic de Broglie wave.
• This means that spacetime is either highly unstable or its fluctuations undergo a scale-dependent super-luminal propagation.