Four Questions on vacuum phase transitions in the Universe...

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Suekdccia
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4 Questions on vacuum phase transitions in the universe...?
I am interested in the topic of vacuum phase transitions in models of the universe. One popular instance of this is a vacuum decay from a metastable vacuum energy level to a "true" one (in which the vacuum would sit at the lowest possible energy level depending on the model)


I have 4 questions on this topic, although it's okay if I get an answer that does not cover all of them necessarily:


1. I have read that there can be both down-tunneling and up-tunneling events (although the up-tunneling events are very suppressed) there are terminal vacua (like AdS or Minskowski spaces) that cannot up-tunnel to any vacua (https://digital.csic.es/bitstream/10261/87436/1/Schellekens.pdf ; page 47). However, if two vacuum bubble events collide, the resultant energy could trigger an up-tunneling of the vacuum, and this could happen between two bubbles of terminal vacua (https://arxiv.org/pdf/1005.3506). However, the new vacuum could not have a higher energy level than the parent vacuum; but if the terminal vacuum bubbles that collided had a zero energy level, then how can there be an up-tunneling to a higher energy level?


2. Can black holes trigger a vacuum phase transition? Can they have enough Hawking temperature to trigger a thermal phase transition? Or perhaps a slow phase transition (https://arxiv.org/pdf/2310.06901 ; https://inspirehep.net/literature/249056)?


3. A vacuum phase transition catalized by particle collisions is rather suppressed as this shows (https://arxiv.org/abs/2301.03620). However does this apply only at the present state of the universe? I mean, will it be also suppressed in the far future once the universe is approaching heat death and almost all what is left are quantum fluctuations? (I did a similar question some days ago, but I would like to focus it on the far future instead of the present universe)


4. Does the energy content of the universe have any influence in vacuum phase transitions? I mean, if there's enough energy/mass content in the universe, could it up-tunnel to a higher vacuum energy level (compared to a universe with almost no energy/mass content)? Perhaps if there is enough energy/mass content in the universe some kind of quantum fluctuation could cause the vacuum to be in a higher energy level (transforming it into a metastable one)? Or this is nonsense and the energy content of the universe is completely unrelated to vacuum phase transitions?
 

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