One of the questions in physical cosmology is, "why is there so little antimatter/matter mixing in the cosmos?". We can measure the mixing by looking for the annihilation spectrum (e.g. e+ e- -> 511 keV/c^2, which for distant extragalactic sources should redshift with the expansion of space). We can produce lots of e+ (positrons) and other antimatter here in laboratories, and so have a fair chunk of the total annihilation spectrum. We also have the spectra of lots and lots of galactic objects (stars, neutron stars, and so forth) and spectra from extragalactic events large (neutral hydrogen clouds) to small (supernovae). There is essentially no sign of known matter-antimatter interaction.

Our galaxy and other members of its cluster are, to high confidence, made essentially entirely of matter.

We have not yet totally precluded distant isolated galaxy clusters made essentially of antimatter, but the cosmic ray spectrum (we see lots of particles that originate at cosmological distances) puts increasingly strong constraints on the distribution and density of such galaxies: there aren't many in total, there's no dense blob of them. The oldest galaxies that we can obtain spectra are also closer together, and each non-observation of annihilation spectral lines puts ever-tighter constraints on other old galaxies' antimatter/matter mix. It is fairly safe to bet that there is simply no significant blob of antimatter in the observable universe, and that what antimatter there is comes from nuclear decays and high-energy astrophysical processes, and all of this antimatter quickly annihilates spatially near where it's produced.

However, that raises a trio of questions. (1) Did some process strongly disfavour the production of antimatter in the early universe, when hydrogen and helium was being produced in abundance? (2) if (1) is true, what is the nature of that process, and how could we see it experimentally? (3) if (1) is not true, where did all the antimatter go? There is an inversion of (3) as well: why didn't the disappearing antimatter take all the matter with it too?

The above is the essence of "the missing antimatter problem" or "the matter-antimatter asymmetry problem" or "baryon asymmetry" <https://en.wikipedia.org/wiki/Baryon_asymmetry> (that last name is for technical reasons, including that there are lots of antineutrinos, anti-photons (which are just photons), and (somewhat complicatedly) anti-gluons and antiquarks [endnote 1] in our universe) and there is a substantial academic literature by experimentalists and theorists.

A family of that literature explores the idea of segregation: matter and antimatter had similar abundances but were driven apart by some process in the early universe. The result is that there will be large (observable-universe-size-or-bigger) regions dominated by antimatter, and large regions (like ours) dominated by matter. But what is the nature of the process?

A subfamily exploring that last question considers the possibility that the segregating interaction is gravitational; a sub-sub-family considers that a change of sign of quantum spin can generate a gravitational difference. One approach to this is to treat quantum spin as a generator of the spin tensor in a modification of General Relativity in which the spin tensor generates the torsion tensor. In General Relativity there is no spacetime torsion at all, so in "semiclassical gravity" where one adds quantum fields to General Relativity (e.g. as in Stephen Hawking's famous 1974 "Black hole explosions?") matter and antimatter gravitate identically. Introducing non-vanishing spacetime torsion can change the nature of black holes enough that black hole evaporation could be very different. And if one couples particle spin to torsion, one could distinguish a black hole created by significant antimatter from a black hole created by practically no antimatter, and we would expect that to show up in the spectra of active galactic nuclei (generated by supermassive black holes) and in the gravitational wave detections of black hole mergers and black hole-neutron star collsions.

Apart from the lack of observational support (which one could sidestep by saying that there is basically no antimatter available to large black holes because it was all chased out of the observable universe by spacetime torsion effects), this quantum spin = spacetime torsion approach runs into a number of theoretical problems. The anti-hydrogen experiment that's the subject here adds a further problem that would need solving. Why would antimatter-matter gravitation today work differently from antimatter-matter gravitation in the early universe? If they work the same, then this experiment makes it unlikely that gravitational repulsin from torsion could solve the missing antimatter problem via early segregation.

This antihydrogen result also imperils proposals for theories of quantum gravity wherein quantum spin (other than that of the graviton or its string equivalent) is gravitationally relevant (but not necessarily arising in that family of string theories especially to solve the missing antimatter problem, i.e., "our theory has a gravitational spin-antispin term in the action which we don't mind because maybe it's too small to matter or maybe if it's big at high energies (like in the hot dense early universe) it can solve a big problem like the missing antimatter problem", essentially).

Finally, wikipedia has a so-so page which is at least reasonably accessible and equipped with a good references section: https://en.wikipedia.org/wiki/Gravitational_interaction_of_a...

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[1] https://profmattstrassler.com/articles-and-posts/largehadron...

"The standard shorthand, “the proton is made from two up quarks and one down quark”, is really a statement that the proton has two more up quarks than up antiquarks, and one more down quark than down antiquarks. To make the glib shorthand correct you need to add the phrase “plus zillions of gluons and zillions of quark-antiquark pairs.” Without this phrase, one’s view of the proton is so simplistic that it is not possible to understand the LHC at all." (for which see a later followup, <https://profmattstrassler.com/articles-and-posts/largehadron...>)