Quartet-Metric Gravity and Dark Components of the Universe

In the report there are presented the general frameworks for the quartet-metric gravity based on the two main principles. First, there exist in space-time the distinct dynamical coordinates, given by a scalar quartet, playing the role of the Higgs fields for gravity. Second, the physical gravity fields arising due to the spontaneous symmetry breaking serve as the dark components of the Universe. It is argued that the mere admixture to metric of the scalar quartet may give rise to an extremely wide spectrum of the emergent gravity phenomena beyond General Relativity (GR). Further developing the proposed frameworks to find out the next-to-GR theory of gravity is a challenge.