Observational bounds on extended theories of gravity from energy conditions

The attempt to describe the recent accelerated expansion of the universe includes different propositions for dark energy models and modified gravity theories. Establish their features in order to discriminate and even rule out part of these models using observational data is a fundamental issue of cosmology. In the present work we consider a class of extended theories of gravity (ETGs) that are minimally coupled to the ordinary matter fields. In this context, and assuming a homogeneous and isotropic spacetime, we derive the energy conditions for this ETG class, which provide bounds for the ETG modifications. We then put constraints on these bounds using a model-independent approach to reconstruct the deceleration function along with the Joint Light-curve Analysis (JLA) supernova sample, 11 baryon acoustic oscillation and 22 cosmic-chronometer measurements. We also obtain an additional bound imposing the strong energy condition only on the ordinary matter. The main result of this work is a set of bounds that every considered ETG must fulfill given the aforementioned assumptions. We apply these bounds to verify the fulfillment/violation of the energy conditions in the context of general relativity. For instance, the strong energy condition is violated, corresponding to an accelerated expansion, with more than $5.22\sigma$ confidence interval considering the whole reconstruction interval. Finally, we show how these bounds can restrict the dynamics of the ETGs by imposing general assumptions on the ETG effective energy density. In this case, there is a preference for a phantom like behavior depending on how this quantity evolves.