Speaker
Description
Lovelock’s hypotheses are a set of reasonable conditions one can impose on the gravitational action that hugely narrow the set of possible gravity theories. In four dimensions, and for a Lorentzian space-time manifold, the set of gravity theories reduces to just one: General Relativity. This incarnation of the Ockham’s razor philosophy has influenced in one way or another the research on the foundations of gravity and modified gravity theories for over fifty years. One of the hypotheses, not explicitly declared as such by Lovelock, is that the space-time manifold is Riemannian. In this work, we have extended Lovelock’s work to spacetimes that enjoy an affine structure fully independent of the metric one, i.e., to spacetimes that not only exhibit curvature but also torsion and non metricity. We fully recover Lovelock’s results as well as Mardones and Zanelli’s torsionful extension of Lovelock’s work in the appropriate limits. Furthermore, our results indicate that, in four dimensions, torsion and non-metricity do not propagate as independent dynamical degrees of freedom, leaving only two propagating degrees of freedom.