  The standard relation between the cosmological redshift and cosmic scale
factor underlies cosmological inference from virtually all kinds of
cosmological observations, leading to the emergence of the LambdaCDM
cosmological model. This relation is not a fundamental theory and thus
observational determination of this function (redshift remapping) should be
regarded as an insightful alternative to holding its standard form in analyses
of cosmological data. Here we present non-parametric reconstructions of
redshift remapping in dark-matter-dominated models and constraints on
cosmological parameters from a joint analysis of all primary cosmological
probes including the local measurement of the Hubble constant, Type Ia
supernovae, baryonic acoustic oscillations (BAO), Planck observations of the
cosmic microwave background (CMB) radiation (temperature power spectrum) and
cosmic chronometers. The reconstructed redshift remapping points to an
additional boost of redshift operating in late epoch of cosmic evolution, but
affecting both low-redshift observations and the CMB. The model predicts a
significant difference between the actual Hubble constant, h=0.48+/-0.02, and
its local determination, h_obs=0.73+/-0.02. The ratio of these two values
coincides closely with the maximum expansion rate inside voids formed in the
corresponding open cosmological model with Omega_m=0.87+/-0.03, whereas the
actual value of the Hubble constant implies the age of the Universe that is
compatible with the Planck LambdaCDM cosmology. The new dark-matter-dominated
model with redshift remapping provides excellent fits to all data and
eliminates recently reported tensions between the Planck LambdaCDM cosmology,
the local determination of the Hubble constant and the BAO measurements from
the Ly-alpha forest of high-redshift quasars.
