Modified Friedmann equations in R  1 -modified gravity

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Abstract
Recently, corrections to the Einstein–Hilbert action that become important at small curvature have been proposed. We discuss the first-order and second-order approximations to the field equations derived by the Palatini variational principle. We work out the first- and second-order modified Friedmann equations and present the upper redshift bounds when these approximations are valid. We show that the second-order effects can be neglected in the cosmological predictions involving only the Hubble parameter, e.g. the various cosmological distances, but the second-order effects cannot be neglected in the predictions involving the derivatives of the Hubble parameter. Furthermore, the modified Friedmann equations fit the SNe Ia data at an acceptable level.