  The multi-measures model applied to cosmology has been recently shown to
reproduce qualitatively the expected stages of the Universe evolution, along
with some unexpected features. In this article, we continue its exploration
with a detailed study of the effective potential of the model. An analysis of
the limits of applicability of the effective potential show that during most of
the Universe evolution, the effective potential is a very good approximation of
the actual potential term. There is, however, a deviation between the two
occurring in the earliest moments of the evolution, which has an important role
on the behavior of the inflaton scalar field. In the studied cases, during this
initial time, the inflaton is increasing in absolute value, which seems
consistent with "climbing up" the effective potential. To investigate this
behavior, we use numerical integration to find the numerical potential and we
show that during the early stage of the evolution, the shape of the numerical
potential is very different from that of the effective one and instead of a
left plateau followed by steep slope, one observes only a slope with additional
local maximum and minimum. This result demonstrates that for complicated
equations of motion of the inflaton, one should not rely only on the notion of
kinetic and effective potential terms to describe the problem as they may not
be accurate in the entire numerical domain.
