Abstract
We consider the cosmology where some function of the Gauss-Bonnet term is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general gravitational theories. It is pointed out that, despite their fourth-order character, such gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard paradigm with cannot be realized in gravity theories unless is a true cosmological constant because it imposes exclusionary constraints on the form of . We analyze the perturbation equations and find that, as in the model, the stability of early-time perturbation growth puts some constraints on the functional form of , in this case . Furthermore, the stability of small-scale perturbations also requires that not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative cosmic history. Our results show how the models are highly constrained by cosmological data.
- Received 25 May 2007
DOI:https://doi.org/10.1103/PhysRevD.76.044027
©2007 American Physical Society