Cosmological perturbation in f(R, G) theories with a perfect fluid
(2010) Physical Review. D, Particles, Fields, Gravitation and Cosmology — Vol. 82, n° 6 (2010)
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- 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 nonrelativistic de Broglie wave. This means that spacetime is either highly unstable or its fluctuations undergo a scale-dependent superluminal propagation. Two other modes correspond to the degrees of freedom of the perfect fluid, and propagate with the sound speed of such a fluid. The remaining two modes correspond to the entropy and temperature perturbations of the perfect fluid, and completely decouple from the other modes for a barotropic equation of state. We then provide a concise condition on f(R, G) theories, which both f(R) and R + f(G) do fulfill, to avoid the de Broglie-type dispersion relation. For the vector-type perturbation, we find that the perturbations decay in time. For the tensor-type perturbation, the perturbations can be either superluminal or subluminal, depending on the model. No-ghost conditions are also obtained for each type of perturbation.
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De Felice, A., Gérard, J.-M., & Suyama, T. (2010). Cosmological perturbation in f(R, G) theories with a perfect fluid. Physical Review. D, Particles, Fields, Gravitation and Cosmology, 82(6). https://doi.org/10.1103/PhysRevD.82.063526 (Original work published 2010)