Lookback time bounds from energy conditions

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.