Generalized gravitational theories from the Lagrangian formulation for non-conservative systems.
Einstein’s general relativity is a theory that has triumphed a lot, passing several tests. However, when it comes to the accelerated expansion of the universe, it is necessary to introduce some type of exotic matter, whose physical term is dark energy. Due to the mysterious nature of dark energy, several models have been proposed as an attempt to avoid it. However, some of such models break the general covariance. The aim of the rpesent work is to propose modified gravitational theories that are deductible from the variational principle. In particular, we will study metric gravity theories derived from Herglotz’s variational principle, which generalizes Hamilton’s principle assuming that the Lagrangean also depends on action. This method is particularly interesting to describe dissipative mechanical systems, but it can also be applied to field theories. We will also see some cases of metric theories derived from minimally modified Lagrangeans which include first order derivatives of the Ricci scalar. In addition to deriving the field equations in each case, some applications of the theories are also made for cosmological models and in the linear approximation of the theory.