Inconsequence in Lawrence Krauss lecture

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Lawrence Krauss discusses the expansion of the universe, explaining that in a flat universe with zero dark energy, expansion slows but never stops. He later contrasts this with a flat universe that includes dark energy, which experiences accelerating expansion. The discussion raises questions about the implications of gravitational potential at infinite distances, suggesting that as the universe expands, the overall negative energy from gravitational interactions may decrease. This leads to concerns about the validity of using infinities in cosmological models. The conversation highlights the complexities of understanding energy dynamics in an ever-expanding universe.
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Hi!

I just found that vide on Youtube:

http://www.youtube.com/watch?v=veU6hK3jMH4&feature=watch-vrec

And something is not quite ok for me. In ~1:00 Krauss says, that in flat universe model universe would expand slower and slower but would never quite stop expanding. On the other hand, in last 4 minutes he says that energy of the vacuum would would cause accelerating expansion of the universe (which is a feature of open universe, like he says in the begining), which is flat at the same moment. How is that consistent?
 
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Early in the video, Krauss talks about universes for which dark energy/cosmological constant is zero. In this case, a "flat universe model universe would expand slower and slower but would never quite stop expanding."

Later in the video, Krauss talks about universes for which dark energy/cosmological constant is non-zero. In this case, at late times, a flat universe has "accelerating expansion".
 
Thanks for answering my question!

Ok, I get this one now, even though I think that he should do some clear remark on that.

Now i come up with another question. Maybe it's lame, but it's bothering me a bit. There is a 'deal' between physicists, that graviataional potential at infinite distance is zero. Let us consider the Universe that is ever expanding without a limit. At some point, if we wait for an infinite period of time, all lumps of mater would be at infinite distances from each other. Therefore overall negative energy of gravitational interaction would 'leak out' of the Universe. How is that?
 
Inserting infinities into the mix is a good way to get invalid results.
 
I mentioned the infinity, but in fact if there is an overall expansion and in general things are getting further and further from each other then energy of gravitational interaction is decreasing even in finite distances. If Univerese was made of three big lumps and the distance between them was increasing, then overall energy of sustem of those three lumps of mater would be decreasing, wouldn't it? I'm aware of the fact that locally sometimes density increases, but all in all Universe becomes less dense if it's meant to expand. So how about it, even without the infinities?
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
Why was the Hubble constant assumed to be decreasing and slowing down (decelerating) the expansion rate of the Universe, while at the same time Dark Energy is presumably accelerating the expansion? And to thicken the plot. recent news from NASA indicates that the Hubble constant is now increasing. Can you clarify this enigma? Also., if the Hubble constant eventually decreases, why is there a lower limit to its value?
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