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The tension between the Hubble constant obtained from the local measurementsand from cosmic microwave background (CMB) measurements motivated us toconsider the cosmological model beyond $\Lambda$CDM one. We investigate thecosmology in the large scale Lorentz violation model with non-vanishing spatialcurvature. The degeneracy among spatial curvature, cosmological constant andcosmological contortion distribution makes the model viable in describing theknown observation date. We get some constraints on the spatial curvature by thecomparison of the relation between measured distance modulus and red-shift withthe predicted one, the evolution of matter density over time and the evolutionof effective cosmological constant. The performance of large scale Lorentzviolation model with non-vanishing spatial curvature under these constrains isdiscussed.

Spatial Curvature and Large Scale Lorentz Violation