Seems like a lot of people are confused by the time/space dilemma in Eureka Seven Ao. Well, here is some explanation based on my observation and interpretation.
1. The scub coral resolving the limits question
They didn't go back in time in the same universe/space, that would disrupt the continuum and but still not solve the problem. Precisely because the scubs understood what humans wanted, at the end of of E7, they went to other universes that are parallel to Eureka Seven's universe. But one of the universe/space they travelled to (namely the distant future of Ao's planet) activated its defense mechanism – the secrets – in order to destroy the scubs. The scub corals then went back to the past of Ao's planet to where there were no secrets, but the secrets travelled through the time portal left behind by the scubs, and the phenomenon known as scub burst began. Therefore the universe in the original E7 was never altered by the events in Ao.
The loophole in this whole thing isn't what the scub corals did, but how Ao ended up in the universe he was in. I guess somehow Renton and Eureka found a way to travel to other universes, that would explain how Eureka, who was pregnant with her first child at that time, appeared in Ao's universe with the gekko. When their first child died, I think Eureka realized who Ao was and the fact that the scubs have traveled to Ao's timeline (the distant past of the planet that is parallel to the one in E7). Then later we see Renton and Eureka, who was pregnant with Ao, trying to destroy the scubs in the distant future so they don't travel to the past in the first place. This is when Renton sends Eureka to the past of this planet so she can give birth in the trapar-less environment, where scub burst happened 10 years later when Renton apparently failed to prevent the scub corals from the distant future to travel to the past.
This explains three things
1. While Eureka was going into labor, she told Fukai Renton is fighting for their child.
2 . Renton said he should be the one to apologize in Ep23, after he meets the apparition of Eureka. Because of his failure, she had to take it upon herself to protect Ao's timeline and by doing so, she was stuck in time/space limbo.
3. Renton knew Ao's name when they first met.
3. Renton knew Ao's name when they first met.
So the idea is circular, Eureka finds out she will give birth to Ao after meeting Ao, and Eureka being sent to the past to give birth to Ao. We don't know if the past determined the future or the future past. In other words, while knowing the existence of Ao, if Eureka and Renton decided to not have a second child after the first died, then Ao's existence would have been erased. At least that's what I think. Bones never made it explicit, so the gaps are left to your own imagination.
3. Eureka time/space limbo
Quartz is basically the mechanism of the scubs that allow them to space travel. Before the scub burst could happen, Eureka attempted to take the quartz somewhere else, however she merely expressed the wish of traveling to a different time and space, but did not specify which timeline and space. As a result, she was unable to materialize and unable to remain in one timeline.
4. Quartz Gun
Renton told Ao that he was going back to the future to destroy the first scub that appeared in this universe. He did not mean his own universe, but the future of Ao's universe. But the implication is that by erasing the scubs, those who were already infected with the coral substance would likely disappear as well. Ao rejected this idea and went for the third option, which is changing the mechanism of the world. After he fired the Quartz gun, it seems like scub burst no longer happened in the newly altered world. My take on this is that secrets, the anti-virus of this world, ceased to exist, and therefore the scubs who traveled to this universe from Eureka's universe in the distant future did not have a need to travel to the past now that nothing is trying to destroy them. Since scub burst didn't happen, Naru and coral carriers were not infected and Elena is probably back in her own time.
[Before Ao fired the Quartz Gun the third time, I am a bit confused to when Eureka saved Elena.....]
Well, I think this is as much as I can sort out. Just how much did the Quartz gun changed the world and sequences of change that took place, we will never find out. It's best to have suspension of disbelief and accept the outcome if things were to make sense.
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Link to Full Review