• emergent cosmology
• quantum gravity

The efforts to develop a theory of Quantum Gravity (QG) questioned the fundamental notions of space and time. This gave rise to the idea that classical spacetime and cosmological dynamics are emergent phenomena. This is also motivated by the unsolved problems of modern cosmology, such as the nature of the observed cosmological acceleration.
The hydrodynamics on (mini)superspace framework allows to make a correspondence between relationally evolving cosmological observables and hydrodynamic averages. In an emergent gravity picture, the hydrodynamic theory can be understood as an effective description emerging from the collective behavior of more fundamental QG building blocks. Group Field Theory (GFT) is a QG theory that offers such a coarse-grained description.
In this work, we explored this correspondence by imposing cosmological conditions on the relational dynamics in order to constrain the hydrodynamic model. In the first part of the analysis, we focused on reproducing different cosmological regimes, including the Friedman, accelerated expansion, de Sitter and asymptotic de Sitter phases. In the second part, we expressed the cosmological dynamics of f(R) modified gravity in relational terms and we determined the conditions under which a hydrodynamic model in a single mode domination regime can reproduce the same observable dynamics.
This work represents a starting point to elaborate a map of the parameter space of a hydrodynamic theory describing an emergent cosmology, with the aim of classifying its regions based on which cosmological dynamics they can reproduce. The approach we introduced allows to further explore the hydrodynamic models that can reproduce different cosmological regimes as well as the dynamics of modified gravity theories, highlighting the universality of the hydrodynamics on minisuperspace framework.