• cosmology
• dark energy
• modified gravity
• unimodular gravity
• energy non-conservation
• quantum gravity phenomenology
• diffusion
• inflation
• hubble tension
• cosmological constant problem
• infation with no inflaton
• hidden sector
• quantum gravity defects

Mounting observational data confirm that the energy density in our Universe mostly consists of dark energy which is responsible for the observed accelerated expansion. The debate around the origin of dark energy is one of the most fascinating unsolved puzzles of modern science and it has branched into several vibrant research lines within the realm of theoretical cosmology and theories of gravitation.

In 2016, a new approach to the problem has been proposed, interpreting dark energy as the consequence of energy dissipation processes which would emerge from more fundamental physics. If successful, this approach would open a new channel of quantum gravity phenomenology, explain the origin of dark energy and at the same time provide a new model of cosmology.

Remarkably, certain dissipation models in Unimodular Cosmology have been shown to solve some of the most debated open problems of standard cosmology, including the cosmological constant problem, the Hubble tension and inflation with no inflaton. However, those particular models are rather speculative and they are often based on mere assumptions and ans ̈atze, while a more complete and fully formal analysis of the underlying dissipation mechanism is still missing.

The goal of this thesis is precisely to determine a rigorous method to implement diffusion in Unimodular Gravity via a formal study of its action taking into account the deep origins of the phenomenon.
To summarize our results, we developed the most general recipe to obtain a non-trivial theory of Unimodular Cosmology and we have derived the full dynamics in the simple case of an ohmic interaction.