How does BBT resolve away from "It should be a black hole"

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AshPowers
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TL;DR
Shouldn't it?
If it all started with a big bang of incredible density and energy, does that mean there must be particles that can travel faster than light? How would anything escape the grip of that kind of gravity? I was under the impression that at a certain threshold of mass/density, it turns into a black hole, right? How did the emergence/early universe just skip past this? Or spring out of it? What is the explanation here?
 
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AshPowers said:
Summary: Shouldn't it?
No.
If it all started with a big bang of incredible density and energy
Yes, but that was not a point in space, it was a point in time so it was nothing like an "explosion"
, does that mean there must be particles that can travel faster than light?
No, there's no need to posit that. Things moved away from each other faster than light but there was little or no proper motion so no speeding tickets were issued. I suggest the link in my signature
How would anything escape the grip of that kind of gravity?
Because it was the same in all directions, so no "escape" was necessary
I was under the impression that at a certain threshold of mass/density, it turns into a black hole, right?
Yes but not when EVERYTHING around it has the same density. What direction would it move?
How did the emergence/early universe just skip past this? Or spring out of it? What is the explanation here?
See above

These are all trivial concerns that have been discussed here many hundreds of times. I suggest that you do a forum search, and just study some really basic cosmology.
 
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AshPowers said:
I was under the impression that at a certain threshold of mass/density, it turns into a black hole, right?

An object that is static will collapse into a black hole if it is compressed enough (enough mass enclosed in a small enough sphere). But the early universe was not static; it was expanding rapidly. So it was a very different condition from the conditions that form a black hole.