I Photon BEC: Hypothetical Universe End-State

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If we pose a hypothetical universe end-state very cold, where only very low energy photons are left. Could these photons undergo a phase transition into something like a BEC?

Would they gain invariant mass if they did (become a condensate) Could someone show why this would/would not happen?

I won't ask what happens if/when we reach Planck Length, I expect this is touchy, so we will simply say information is lost here. I only want to explore what happens just above this. All input appreciated.
 
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May I "answer" your question by rejecting the hypothesis?

I don’t think that this ‘Heat death of the universe’ hypothesis is the correct theory in the first place. Black holes can’t just disappear (black holes can only decrease in size/mass when Hawking radiation occurs, which of course brings us back to the creation photons again). Photons are attracted by black holes, even though they are massless, so at some point these far away low energy microwave photons could "feel" the attraction back towards the gravitational pull of these black holes, instead of expanding into infinity, or having to condensate as the only one remaining possibility. There's no evidence that suggests that the dynamics in the universe could not be an everlasting cycle.
 
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Hawking Radiation is clever, but I want to pose a hypothetical scenario without. I knew this was the fist thing that would haunt, it is the thorn in the side -a universe eventually dominated by Hawking's clever notion. For now, let's leave this out and assess. I know this will lead to me being a hypocrite, but we will ignore this due to lack empirical observation, at least for now. We can explore Hawking Radiation later... You are probably correct in stating that there is no reason it can't be an everlasting cycle, but I want to explore this here first, then later explore a condensate as a pre-universe state also.
 
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