For decades, the scientific community has recognized that our universe is expanding at an accelerating rate (Riess A. G. et al., 1998); however, in some respects, cosmology has not taken this into account. The FLRW metric assumes that time has always passed in the same way at every moment and place, that is, that the Lapse function is equal to one. In recent years, this problem has been studied in greater depth (Melia, F., 2019, 2023), demonstrating that a Lapse function equal to one is only valid for non-accelerating universes and not for accelerating ones. Therefore, errors are made when referencing times to reference frames with a Lapse function equal to one, so these times are not the true times. It is necessary to find an inertial reference frame in our accelerating universe that allows us to determine times correctly, and to find it, we must modify the Lapse function. In this work, we have studied what the Lapse function should be in order to lead to a free-fall reference frame and in it determine the true times of the ages of galaxies.