Sabine Hossenfelder has a slightly tongue-in-cheek FAQ on anti-gravitation, and from time to time blogs about it. https://fias.uni-frankfurt.de/~hossi/Physics/

Sabine Hossenfelder has a slightly tongue-in-cheek FAQ on anti-gravitation, and from time to time blogs about it. https://fias.uni-frankfurt.de/~hossi/Physics/anti-gravity.html https://fias.uni-frankfurt.de/~hossi/Physics/anti-gravity.ht... You might find that interesting. The key constraints come from General Relativity; the successes of the Schwarzschild and Kerr(-Newman) metrics for physically plausible arrangements of matter need to be preserved if you try to add in a symmetry. If we use perturbation theory to capture deviations from the metric of a reasonable exact solution to the Einstein Field Equations, the structures can be represented as classical waves in the metric tensor. Quantizing these waves ("perturbatively quantized gravity") inevitably results in a massless spin-2 particle. Spin-2 interactions have a feature you wrote yourself: > that like attracts like, and unlike repels unlike (maybe more clearly put as: like charges mutually attract and unlike charges mutally repel). Note that this is backwards from the spin-1/2 of fermions. > "Dark matter" would be variation in the prevalence of one sign or the other. In the standard cosmology, dark matter is attractive. Ordinary matter falls into areas where dark matter is dense, as discussed in the "Unprecedently wide and sharp dark matter" phys.org article, or if you prefer, http://www.esa.int/Our_Activities/Space_Science/Planck/History_of_cosmic_structure_formation http://www.esa.int/Our_Activities/Space_Science/Planck/Histo... If you want a particle which interacts gravitationally with ordinary matter but which can carry a gravitational charge of opposite sign, you probably shouldn't call it "dark matter". However, you can certainly define such a thing with some rigour and test it. > How would one test such a model? Mathematically? After all, you need to generate reasoned (rather than guessed) observables that you can then look for. You would probably do like Noether and Hilbert and solve the equations of motion of your matter theory producing the canonical stress-energy tensor, and then improve it using a metric variational procedure. Forger & Römer is a good place to look: https://arxiv.org/abs/hep-th/0307199 https://arxiv.org/abs/hep-th/0307199 You can see how Hossenfelder does this in her anti-gravitation paper (direct link: https://arxiv.org/abs/gr-qc/0508013 https://arxiv.org/abs/gr-qc/0508013) in which her matter theory doubles the number of particles in the Standard Model, with the second set identical to the first except for the opposite gravitational charge); Forger & Römer is her reference [20]. Once you have a self-consistent and reasonably complete model you can consider areas where it generates identical observables to the standard cosmology where those are already being tested (the fine detail in the cosmic microwave background; gross structures like galaxies, clusters, and filaments; large-scale homogeneity and isotropy; the Hubble flow) and where your model makes predictions that differ from the standard cosmology.