  At a global scale, the universe is generally fitted by an idealized manifold
described by the FLRW metric. This is in particular the case when probing the
universe to determine its dynamics. The process that fits the idealized
manifold to the real universe is however not uniquely defined. This process may
depend on the cosmic probe that has been used for the measurements, and could
hence lead to different observed temporal evolutions of the scale factor. A
correct interpretation of the observed accelerated expansion of the universe
requires therefore first a thorough understanding of the fitting process that
has been implicitly applied. In this article we establish the fitting processes
for the SNIa, BAO and CMB cosmic probes, and deduce the related averaged
Einstein equations. We demonstrate that the way these fittings have been
applied in practice lead to an apparent dark energy effect. We also highlight
the conceptual differences in the fitting processes between the SNIa and BAO
probes on the one hand, and the CMB probe on the other hand. Considering those
differences, we then show how the so-called Hubble tension can be explained.
