  In general relativity, the energy conditions are invoked to restrict general
energy-momentum tensors on physical grounds. We show that in the standard
Friedmann-Lemaitre-Robertson-Walker (FLRW) approach to cosmological modeling,
where the energy and matter components of the cosmic fluid are unknown, the
energy conditions provide model-independent bounds on the behavior of the
lookback time of cosmic sources as a function of the redshift for any value of
the spatial curvature. We also confront such bounds with a lookback time sample
which is built from the age estimates of 32 galaxies lying in the interval
$0.11 \lesssim z \lesssim 1.84$ and by assuming the total expanding age of the
Universe to be $13.7 \pm 0.2$ Gyr, as obtained from current cosmic microwave
background experiments. In agreement with previous results, we show that all
energy conditions seem to have been violated at some point of the recent past
of cosmic evolution.
