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Constraints on hybrid metric-Palatini models from background evolution

In this work, we introduce two models of the hybrid metric-Palatini theory of gravitation. We explore their background evolution, showing explicitly that one recovers standard General Relativity with an effective Cosmological Constant at late times. This happens because the Palatini Ricci scalar evolves towards and asymptotically settles at the minimum of its effective potential during cosmological evolution. We then use a combination of cosmic microwave background, supernovae and baryonic accoustic oscillations background data to constrain the models' free parameters. For both models, we are able to constrain the maximum deviation from the gravitational constant $G$ one can have at early times to be around $1\%$.