Ludovic Ducobu (UNamur)

In this talk, I will present recent results of my work in cosmology and variational geometry.

I will review basic notions in variational geometry and present the method of variational completion, allowing to reconstruct a Lagrangian for a theory from a guess of its field equations.

I will then show how this can be extended to theories that involve at least two sets of dynamical variables.

This new method, introduced in [1] and called variational bootstrapping, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set.

This setup is particularly appealing for the construction of modified theories of gravity, since one can take lessons from General Relativity for an “educated guess” of the metric field equations; the field equations for the other fields are then fixed by the obtained Lagrangian (up to terms that are completely independent from the metric tensor).

To conclude, following [2], I will show how one can apply variational bootstrapping to determine metric-affine models which are, in a variational sense, the closest to the ΛCDM model of cosmology : starting from an “educated guess” that formally resembles the Einstein field equations with a cosmological constant and a dark matter term, the method allows to find “corrected” metric equations and to “bootstrap” the connection field equations.

This presentation is based on the work done in [1] and [2] in collaboration with Nicoleta Voicu.