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In the far future, the particle horizon will reach 63 Gly,so when will that time? Just like today's universe time is 13.82 Gyr and the particle horizon is 46.5 Gly, how many years will the particle horizon reach its limit, and we can no longer receive further light?

Is there a related calculation process or scale diagram about the observable universe radius and time?

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The maximum particle horizon size is approached asymptotically over an infinite span of time.

There is no particular time at which the light from distant objects stops reaching us. Rather, the remaining light is stretched (redshifted) into the indefinite future.

When you add quantum mechanics, only finitely many photons in total reach us, and so there is a time at which the last photon arrives. That time is random, but the expected time is probably a smallish multiple of the Hubble time, on the order of 100 billion or 1 trillion years from now.

The distance to the particle horizon at time $t$ is $\displaystyle \int_0^t \frac{c\,dt'}{a(t)}$, and there are diagrams in many Physics SE questions that will show you the particle horizon distance as a function of time, such as this one:

Note that the top of the diagram is $t=\infty$.

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