The Many Faces of General Relativity: Implications for Inflation and Dark Matter

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.

Based on:
M. Shaposhnikov, A. Shkerin, I. Timiryasov, S. Zell,
    Higgs inflation in Einstein-Cartan gravity, JCAP 02 (2021), arXiv:2007.14978;
    Einstein-Cartan Portal to Dark Matter, Phys. Rev. Lett. 126 (2021) 161301, arXiv:2008.11686.
G. Karananas, M. Shaposhnikov, A. Shkerin, S. Zell,
    Matter matters in Einstein-Cartan gravity, Phys. Rev. D 104 (2021) 064036, arXiv:2106.13811.
C. Rigouzzo, S. Zell, Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field, arXiv:2204.03003.