So I know that the particle horizon distance in our universe is about 46 billion light years. I also know that as $t \to \infty$, the particle horizon distance approaches a finite value. What is this value and how can it be calculated?

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    $\begingroup$ See this great answer by Pulsar on the Physics site. As mentioned in that answer, in practice, we can't see beyond the last scattering surface of the CMB (although maybe future technology will be able to detect cosmic neutrinos that were emitted earlier than the CMB). Please note that the finite distance of 62.9 billion light-years is in comoving coordinates, the (so-called) proper distance to the particle horizon isn't bounded, as Pela mentions here. $\endgroup$ – PM 2Ring Oct 13 '20 at 3:57

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