Thought experiment: Communication beyond the particle horizon

[Lanniakea]

Refer to this image: http://imgur.com/xT20HOv

1. The white nodes are 'stations' which broadcast signals at light speed. The blue circles around them represent the particle horizon relative to these nodes.
2. The pink nodes are intermediary stations in between these stations that pass on the signal. The pink circles are their respective particle horizons.
3. All nodes always maintain the same distance relative to each other; they move in a way to negate the expansion of the universe.
4. The number of nodes in the example is arbitrary.

The idea:

A signal is sent from the starting node and reaches the first pink node. From here it is sent toward the next white 'station' node. Now here's the idea: Even though the signal has left the particle horizon of the starting node, the next station's particle horizon includes both white nodes. So while the two white nodes cannot communicate directly, the pink node is in reach for both of them.

The Question: Could the starting and ending node exchange information in a finite amount of time, given that the nodes maintain their relative distances?

Thanks!

 

[Jorrie]

The Question: Could the starting and ending node exchange information in a finite amount of time, given that the nodes maintain their relative distances?

Yes. Particle horizons grow without limit as time goes on. See the Davis expansion graphs: https://www.physicsforums.com/attachments/davisdiagramoriginal2-jpg.55869/

But take note that if your circles are of particle horizon sizes, they are much larger than the Hubble radius and they cannot "hold station", but will instead be receding from each other at a rate exceeding c. Also, they must be within each others cosmological (communications) horizons to ever communicate.