Among the various possibilities to probe the theory behind the recent accelerated expansion of the universe, the energy conditions (ECs) are of particular interest, since it is possible to confront and constrain the many models, including different theories of gravity, with observational data. In this context, we use the ECs to probe any alternative theory whose extra term acts as a cosmological constant. For this purpose, we apply a model-independent approach to reconstruct the recent expansion of the universe. Using Type Ia supernova, baryon acoustic oscillations and cosmic-chronometer data, we perform a Markov Chain Monte Carlo analysis to put constraints on the effective cosmological constant $Omega^0_{rm eff}$. By imposing that the cosmological constant is the only component that possibly violates the ECs, we derive lower and upper bounds for its value. For instance, we obtain that $0.59 < Omega^0_{rm eff} < 0.91$ and $0.40 < Omega^0_{rm eff} < 0.93$ within, respectively, $1sigma$ and $3sigma$ confidence levels. In addition, about 30% of the posterior distribution is incompatible with a cosmological constant, showing that this method can potentially rule it out as a mechanism for the accelerated expansion. We also study the consequence of these constraints for two particular formulations of the bimetric massive gravity. Namely, we consider the Vissers theory and the Hassan and Rosess massive gravity by choosing a background metric such that both theories mimic General Relativity with a cosmological constant. Using the $Omega^0_{rm eff}$ observational bounds along with the upper bounds on the graviton mass we obtain constraints on the parameter spaces of both theories.
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