According to the theory of special relativity as an object approaches light speed it experiences length contraction. This means that the distance it observes between it and it's destination reduces as it's speed increases.
We also know that the universe is expanding. And that the expansion rate depends on the distance between two objects. The further the distance the faster the space between them is expanding. This means that if an object is far enough away the expansion rate of the universe can exceed it's speed meaning that it can never arrive. Beyond the cosmic event horizon space between us and it is expanding at a rate greater then speed of light so even light can never reach us.
However if an object was to travel towards earth from just beyond the cosmic even horizon at speeds approaching the speed of light the length contraction that it observes would bring earth within the cosmic even horizon. In the objects frame of reference it will arrive on earth. But in earths frame of reference it will never arrive.
How does one resolve this paradox?
Does the observed expansion of the universe speed up as an object approaches the speed of light? Do we need to add expansion acceleration to time dilation and length contraction in special relativity?
Is there some other way to resolve this paradox?