Linear perturbations in viable f(R) theories

We describe the cosmological evolution predicted by three distinct f(R) theories, with emphasis on the evolution of linear perturbations. The most promising observational tools for distinguishing f(R) theories from Lambda CDM are those intrinsically related to the growth of structure, such as weak lensing. At the linear level, the enhancement in the gravitational potential provided by the additional f(R) fifth force'' can separate the theories, whereas at the background level they can be indistinguishable. Under the stringent constraints imposed on the models by Solar System tests and galaxy-formation criteria, we show that the relative difference between the models' linear evolution of the lensing potential will be extremely hard to detect even with future space-based experiments such as Euclid, with a maximum value of approximately 4% for small scales. We also show the evolution of the gravitational potentials under more relaxed local constraint conditions, where the relative difference between these models and Lambda CDM could prove discriminating.