  A discrete space-time structure lying at about the Planck scale may become
manifest in the form of very small violations of the conservation of the matter
energy-momentum tensor. In order to include such kind of violations, forbidden
within the General Relativity framework, the theory of unimodular gravity seems
as the simplest option to describe the gravitational interaction. In the
cosmological context, a direct consequence of such violation of energy
conservation might be heuristically viewed a "diffusion process of matter (both
dark and ordinary)" into an effective dark energy term in Einstein's equations,
which leads under natural assumptions to an adequate estimate for the value of
the cosmological constant. Previous works have also indicated that these kind
of models might offer a natural scenario to alleviate the Hubble tension. In
this work, we consider a simple model for thecosmological history including a
late time occurrence of such energy violation and study the modifications of
the predictions for the anisotropy and polarization of the Cosmic Microwave
Background (CMB). We compare the model's predictions with recent data from the
CMB, Supernovae Type Ia, cosmic chronometers and Baryon Acoustic Oscillations.
The results show the potential of this type of model to alleviate the Hubble
tension.
