Thank you for you attention, but unfortunately I was wrong. In a more detailed analysis, I found that the reason for the accelerated expansion of the Universe comes, with the subsequent limitation of this speed by the speed of light, from the essence of the special theory of relativity - the conservation of the interval. But this is true for gravitationally non-interacting bodies. Where this interaction is significant, Newtonian mechanics works there. By the way, the expansion of the Universe does not come from a singularity (big bang), but from a sufficiently large distance determined by the total mass of the Universe. As for Hubble's law, it is an approximation for a small portion of 100/300,000 speeds.
It may seem that the expression for the expansion of the Universe obtained from SRT contradicts the linearity of the Hubble law. But, as I recently found out, the distance itself is obtained from this linearity. An independent determination of this distance requires a synthesized aperture of a million kilometers, which can only be done from satellites using frequency standards.
Thus, there is no linearity in the Hubble law and it can only be valid in the vicinity of small distances.