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We study the properties of dark matter haloes in a wide range of modifiedgravity models, namely, $f(R)$, DGP, and interacting dark energy models. Westudy the effects of modified gravity and dark energy on the internalproperties of haloes, such as the spin and the structural parameters. We findthat $f(R)$ gravity enhance the median value of the Bullock spin parameter, butcould not detect such effects for DGP and coupled dark energy. $f(R)$ alsoyields a lower median sphericity and oblateness, while coupled dark energy hasthe opposite effect. However, these effects are very small. We then study theinteraction rate of haloes in different gravity, and find that only stronglycoupled dark energy models enhance the interaction rate. We then quantify theenhancement of the alignment of the spins of interacting halo pairs by modifiedgravity. Finally, we study the alignment of the major axes of haloes with thelarge-scale structures. The alignment of the spins of interacting pairs ofhaloes in DGP and coupled dark energy models show no discrepancy with GR, while$f(R)$ shows a weaker alignment. Strongly coupled dark energy shows a strongeralignment of the halo shape with the large-scale structures.

Dark matter haloes in modified gravity and dark energy: interaction rate, small-, and large-scale alignment