  This is the first paper of a series aiming at investigating galaxy formation
and evolution in the giant-void class of the Lemaitre-Tolman-Bondi (LTB) models
that best fits current cosmological observations. Here we investigate the
Luminosity Function (LF) methodology, and how its estimates would be affected
by a change on the cosmological model assumed in its computation. Are the
current observational constraints on the allowed Cosmology enough to yield
robust LF results? We use the far-infrared source catalogues built on the
observations performed with the Herschel/PACS instrument, and selected as part
of the PACS evolutionary probe (PEP) survey. Schechter profiles are obtained in
redshift bins up to z approximately 4, assuming comoving volumes in both the
standard model, that is, Friedmann-Lemaitre-Robertson-Walker metric with a
perfect fluid energy-momentum tensor, and non-homogeneous LTB dust models,
parametrized to fit the current combination of results stemming from the
observations of supernovae Ia, the cosmic microwave background, and baryonic
acoustic oscillations. We find that the luminosity functions computed assuming
both the standard model and LTB void models show in general good agreement.
However, the faint-end slope in the void models shows a significant departure
from the standard model up to redshift 0.4. We demonstrate that this result is
not artificially caused by the used LF estimator which turns out to be robust
under the differences in matter-energy density profiles of the models. The
differences found in the LF slopes at the faint end are due to variation in the
luminosities of the sources, which depend on the geometrical part of the model.
It follows that either the standard model is over-estimating the number density
of faint sources or the void models are under-estimating it.
