Metric-affine Geometry and Ghost-free structure of Scalar-tensor Theories

Abstrakt: Scalar-tensor theories in metric-affine geometry are formulated. General Relativity is currently the most successful gravitational theory which has surpassed countless observations. However, in recent years, it has been noticed that GR cannot explain some cosmological phenomena such as inflation, dark energy and dark matter. To solve this, countless alternative gravitational theories beyond General Relativity has been proposed. However, most require the geometry to be Riemannian, just as in GR. In this talk, it will be shown how one could extend theories of gravity by 'deforming' Riemann Geometry into what is called metric-affine geometry, in which not only the metric but also that connection is an independent variable that is decided from the gravitational action. By applying metric-affine formalism to scalar-tensor theories, one notices that there are different and fruitful characteristics that appear when compared to the Riemann counterpart. Especially, through the novel symmetry of the connection called 'projective symmetry', one may find natural ways to eliminate ghosts that are caused by higher derivatives. Finally, some possible applications would be discussed. References: Phys.Rev. D98 (2018) no.4, 044038 Phys. Rev. D 100, 044037 (2019).