The study of dense matter at ultra-high density has a very long history, which is meaningful for us to understand not only cosmic events in extreme circumstances but also fundamental laws of physics. In compact stars at only a few nuclear densities but low temperature, quarks could be interacting strongly with each other. That might produce quarks grouped in clusters, although the hypothetical quark-clusters in cold dense matter have not been confirmed due to the lack of both theoretical and experimental evidence. A so-called H-cluster matter is proposed in this paper as the nature of dense matter in reality.

Motivated by recent lattice QCD simulations of the H-dibaryons (with structure uuddss), we are therefore considering here a possible kind of quark-clusters, H-clusters, that could emerge inside compact stars during their initial cooling, as the dominant components inside (the degree of freedom could then be H-clusters there). We study the stars composed of H-clusters, i.e., H-cluster stars, and derive the dependence of their maximum mass on the in-medium stiffening effect, showing that the maximum mass could be well above 2 M⊙ as observed and that the resultant mass-radius relation fits the measurement of the rapid burster under reasonable parameters. Besides a general understanding of different manifestations of compact stars, we expect further observational and experimental tests for the H-cluster stars in the future.