Cosmological redshift from translations in an Einstein-Milne universe relativity with bounded position and velocity

Milne Universe is one of the models of cosmology that employs hyperboloids as its surfaces of constant time. The special relativistic construction of the model, though very interesting, has problems with the observational data. We suggest a method to modify the model and remedy its issues. The idea is to change the coordinates of the observers from the origin to a distance d in the time direction. It is similar to the velocity 4-vector that does not vanish for an observer at rest and has a component c in the timelike direction. The constant d is an invariant length that acts as a bound for position in the same way that c serves as a bound for velocity. In this regard, translations in space turn out to be boosts, similar to the translations in velocity. In this model, which we call Einstein-Milne, the cosmological redshift is a result of spatial translations via the Doppler effect. We show that the model can explain the Hubble diagram without assuming dark matter and energy, as well as acceleration of the Universe. The Hubble constant is obtained as a function of supernovae Ia absolute magnitude by fitting the predicted Hubble diagram to the data, which provides a means of releasing its tension.