How can the visible universe be 46 billion light-years in radius when the universe is only 13.8 bill

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First of all, we should explain that the light-speed limit that relativity imposes on objects within the universe doesn't apply to the universe itself. In fact, we can't refer to an absolute expansion speed of the universe because we can't measure it in reference to anything external. We can only gauge the "speeds" of distant galaxies that are receding from us relative to our own position. Apart from those that are gravitationally bound (such as, say, the Milky Way and Andromeda galaxies), all galaxies appear to be moving away from each other as the space-time in which they're embedded expands. The more distant the galaxy, the faster its recession velocity, as noted by the Hubble Law. As a consequence of this expansion, a galaxy's location changes considerably during the period of time that its light requires to travel to Us.