Modified Gravity

I am interested in modified theories of gravity. A variety of modified gravity theories have been analysed and it was found that some of these models satisfy cosmological and local gravity constraints and are practically indistinguishable from the ΛCDM model, at least at the background level. There many generalisations of modifications of the Einstein-Hilbert action. For instance, an arbitrary function of the Gauss-Bonnet term in the action yields additional terms in the resulting field equations. Likewise, higher order terms, including squares of the Ricci tensor, the Riemann tensor and the Weyl tensor lead to interesting models. Moreover I am studying models related to the teleparallel equivalent of general relativity.

Continuum mechanics

I am mainly interested elasticity with microrotations, also known as Cosserat elasticity or micropolar elasticity. This field shows some surprising similarities with general relativity. For instance, microrotations can be described using concepts from differential geometry, in particular the torsion tensor. It turns out that the action of microrotations looks like a three-dimensional version of the action of teleparallel gravity. In this context we could find some travelling wave solutions. In these animations the linear movements of the rings indicate the effect of elastic displacements while the rotations indicate the microrotations at these points.