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Starting from the geometrical trinity of gravity I will introduce General Relativity in 3 equivalent geometrical formulations with a special emphasis on Coincident General Relativity. I will show how one could try to move away from GR in these geometrical manifestations of gravity. In the context of cosmological ingredients for dark matter, dark energy and inflation I will introduce scalar and vector degrees of freedom with an emphasis on generalized Proca theories. I will show how with a simple cubic interaction of the vector field the H0 tension can be relieved.
Nicola Bartolo, Daniele Bertacca, Michele Liguori, Sabino Matarrese, Alvise Raccanelli, Angelo Ricciardone