Negatively curved spacetime will drive mass-energy away from each other. It is thought that in the future the expansion of mass-energy will get higher and higher. Because the dilution of mass-energy, the supposed dark energy (this is the same as negatively curved spacetime) will get a higher grip. That is, the situation will be reminiscent of the inflation era of the universe. Can it be that new particles are formed out of virtual particle-antiparticle pairs? Like is the case around black holes as Hawing radiation appears (although there, spacetime is strongly positively curved)? To put is in other words, will spacetime be so negatively curved one day that these particle pairs will be created again (and so effectively a new big bang occurs)?
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It's my understanding that the hypothesized particle formation due to inflation happened at the end of inflation, when the "inflaton field" decayed to produce the "normal vacuum" have now. So unless dark energy is due to a false vacuum that can decay, I'm not sure you'd get any particle formation. – Peter Erwin Jun 10 '21 at 11:46
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@PeterErwin Hi there! Can't it be that the spacetime before the creation of matter was negatively curved? Due to the presence of virtual particle pairs (or vacuum fluctuations of the matter-energy fields)? I can imagine that these particles are driven away so violently from each other that they become real (as is the case for Hawking radiation), thereby making the curvature positive. So they are the cause of negative curvature (when virtual) as well the cause of positive curvature (when real). – Deschele Schilder Jun 10 '21 at 12:06