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Spatial Curvature and Large Scale Lorentz Violation

The tension between the Hubble constant obtained from the local measurements and from cosmic microwave background (CMB) measurements motivated us to consider the cosmological model beyond $Λ$CDM one. We investigate the cosmology in the large scale Lorentz violation model with non-vanishing spatial curvature. The degeneracy among spatial curvature, cosmological constant and cosmological contortion distribution makes the model viable in describing the known observation date. We get some constraints on the spatial curvature by the comparison of the relation between measured distance modulus and red-shift with the predicted one, the evolution of matter density over time and the evolution of effective cosmological constant. The performance of large scale Lorentz violation model with non-vanishing spatial curvature under these constrains is discussed.