Finslerian Universe May Reconcile Tensions between High and Low Redshift
  Probes
  To reconcile the current tensions between high and low redshift observations,
we perform the first constraints on the Finslerian cosmological models
including the effective dark matter and dark energy components. We find that
all 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 Universe
observations at the 68$\%$ confidence level. The addition of a massless sterile
neutrino and a varying total mass of active neutrinos to the base Finslerian
two-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 other
three Finslerian models. Computing the Bayesian evidence, with respect to
$\Lambda$CDM model, our analysis shows a weak preference for the base
Finslerian model and moderate preferences for its three one-parameter
extensions. Based on the model-independent Gaussian Processes, we propose a new
linear relation which can describe the current redshift space distortions data
very well. Using the most stringent constraints we can provide, we have also
obtained the limits of typical model parameters for three one-parameter
extensional models.
