In chameleon dark energy models, local gravity constraints tend to rule out parameters in which observable cosmological signatures can be found. We study viable chameleon potentials consistent with a number of recent observational and experimental bounds. A novel chameleon field potential, motivated by $f(R)$ gravity, is constructed where observable cosmological signatures are present both at the background evolution and in the growth rate of the perturbations. We study the evolution of matter density perturbations on low redshifts for this potential and show that the growth index today ${\gamma }_0$ can have significant dispersion on scales relevant for large scale structures. The values of ${\gamma }_0$ can be even smaller than 0.2 with large variations of $\gamma$ on very low redshifts for the model parameters constrained by local gravity tests. This gives a possibility to clearly distinguish these chameleon models from the $\Lambda$-cold-dark-matter ($\Lambda \mathrm{CDM}$) model in future high-precision observations.

• Received 18 October 2010

DOI:https://doi.org/10.1103/PhysRevD.82.124006