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Here we analysed a particular type of $F(R)$ gravity, the so-calledexponential gravity which includes an exponential function of the Ricci scalarin the action. Such term represents a correction to the usual Hilbert-Einsteinaction. By using Supernovae Ia, Barionic Acoustic Oscillations, CosmicMicrowave Background and $H(z)$ data, the free parameters of the model are wellconstrained. The results show that such corrections to General Relativitybecome important at cosmological scales and at late-times, providing analternative to the dark energy problem. In addition, the fits do not determineany significant difference statistically with respect to the $\Lambda$CDMmodel. Finally, such model is extended to include the inflationary epoch in thesame gravitational Lagrangian. As shown in the paper, the additional terms canreproduce the inflationary epoch and satisfy the constraints from Planck data.

Is exponential gravity a viable description for the whole cosmological history?