Born-Infeldisation of the early universe

In order to regularise the energy of point-like charged particles, Born and Infeld introduced a modification of the Maxwell Lagrangian that naturally imposes an upper bound on electromagnetic fields. Similar ideas can be applied to gravity to resolve the GR singularities. I will discuss some general theoretical aspects of these theories (which are shared by more general metric-affine theories) as well as some cosmological applications, with emphasis in non-singular and inflationary solutions.