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We discuss implications on the $$H_0$$ tension due to preferred-frame effects in the context of Hořava–Lifshitz gravity. By using a combination of low-redshift data (Sne1a, elliptical and lenticular galaxies, GRB’s, and quasars) we discuss the $$H_0$$ tension and its appearance as a preferred-frame effect, as well as present new constraints on the model parameter $$\lambda $$; moreover, from the structure of the Friedmann equations, we argue that up to 36% of the Hubble tension can be explained by Lorentz-violating effects in a Hořava–Lifshitz scenario, and we briefly discuss the cosmographic behaviour of this model.

Preferred-frame effects, the $$H_0$$ tension, and probes of Hořava–Lifshitz gravity