  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, $1\sigma$ and $3\sigma$ 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 Visser's theory and the Hassan and Roses's 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.
