Direct cosmological communication and a shared causal past ($d\le \eta \text{ versus }d\le 2\eta$)

In a spatially flat Friedmann-Lemaître-Robertson-Walker metric with initial conformal time zero, two comoving worldlines at separation $d$ can exchange a one-way light signal by time $\eta$ only if $d\le \eta$. Their past light cones overlap if $d\le 2\eta$: a common event halfway between them can influence both. These are different statements. For opposite emission events observed at conformal time ${\eta }_0$, their separation is $2({\eta }_0-{\eta }_e)$, so the respective thresholds are ${\eta }_e\ge 2{\eta }_0/3$ and ${\eta }_e\ge {\eta }_0/2$.