General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but lead to distinct predictions once other fields are included. First, I will give an overview of various versions of GR and highlight metric-affine gravity, which encompasses the metric, Palatini and Einstein-Cartan formulations as special cases. Generically numerous free parameters arise when matter is coupled (non-minimally) to GR. This has important implications for inflationary scenarios driven by the Higgs field. Predictions are no longer unique but they agree with observations in large parts of parameter space. Finally, I will present a new mechanism for producing fermionic dark matter in the early Universe. It leads to a characteristic primordial momentum distribution, which might be detectable in the case of warm dark matter.
