= Cosmological round-trip communication horizon
{title2=$d_{\mathrm{round}}(t)=\frac{a(t)}2\int_t^\infty\frac{dt'}{a(t')}$}
A light signal sent from a comoving observer to a comoving reflector at separation $\chi$, and immediately returned, consumes <conformal time> $2\chi$. The supremum of the initial physical reflector distances allowing a return is therefore half the <cosmological event horizon> radius. Equality generally requires infinite return time; finite-time reception requires a strictly smaller distance. For a <cosmological domain wall network> with $a\propto t^2$, the supremum is $t/2=1/H$.
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