Restricting fourth-order gravity via cosmology

The cosmology of general fourth-order corrections to Einstein gravity is considered, both for a homogeneous and isotropic background and for general tensor perturbations. It is explicitly shown how the standard cosmological history can be (approximately) reproduced and under what condition the evolution of the tensor modes remain (approximately) unchanged. Requiring that the deviations from general relativity are small during inflation sharpens the current constraints on such corrections terms by some thirty orders of magnitude. Taking a more conservative approach and requiring only that cosmology be approximately that of general relativity during big bang nucleosynthesis, the constraints are improved by 4-6 orders of magnitude.