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To reconcile the current tensions between high and low redshift observations,we perform the first constraints on the Finslerian cosmological modelsincluding the effective dark matter and dark energy components. We find thatall the four Finslerian models could alleviate effectively the Hubble constant($H_0$) tension and the amplitude of the root-mean-square density fluctuations($\sigma_8$) tension between the Planck measurements and the local Universeobservations at the 68$\%$ confidence level. The addition of a massless sterileneutrino and a varying total mass of active neutrinos to the base Finsleriantwo-parameter model, respectively, reduces the $H_0$ tension from $3.4\sigma$to $1.9\sigma$ and alleviates the $\sigma_8$ tension better than the otherthree Finslerian models. Computing the Bayesian evidence, with respect to$\Lambda$CDM model, our analysis shows a weak preference for the baseFinslerian model and moderate preferences for its three one-parameterextensions. Based on the model-independent Gaussian Processes, we propose a newlinear relation which can describe the current redshift space distortions datavery well. Using the most stringent constraints we can provide, we have alsoobtained the limits of typical model parameters for three one-parameterextensional models.

Finslerian Universe May Reconcile Tensions between High and Low Redshift Probes