Does the Universe Really Expand Faster than the Speed of Light: Kinematic Analysis Based on Special Relativity and Copernican Principle

In the first approximation, the Universe’s expansion is described by the Hubble’s law v = H · R, according to which the relative speed v of two objects in the expanding Universe grows linearly with the distance R between them. This law can be derived from the Copernican principle, according to which, cosmology-wise, there is no special location in the Universe, and thus, the expanding Universe should look the same from every starting point. The problem with the Hubble’s formula is that for large distance, it leads to non-physical larger-than-speed-of-light velocities. Since the Universe’s expansion is a consequence of Einstein’s General Relativity Theory (GRT), this problem is usually handled by taking into account GRT’s curved character of space-time. In this paper, we consider this problem from a purely kinematic viewpoint. We show that if we take into account special-relativistic effects when applying the Copernican principle, we get a modified version of the Hubble’s law in which all the velocities are physically meaningful – in the sense that they never exceed the speed of light.