Big Crunch and the Universe's shape

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In summary, if we want to discard the possibility of a Big Crunch, we also have to discard the hypothesis of a spherical universe.
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LCSphysicist
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I was reading a book about cosmology, from Andrew Liddle, where in the chapter 5 he start to talk about implications of the differentes signs possible to k (k from the Friedmann equation). It is said, until this chapter, that the implication of k>0 inevitably implies a stop in the Universe expansion, and eventually a Universe's contraction. But, as far as i know, the Big Crunch was already discarded, so it is the same to say that k can not be greater than 0?
In another words, to discard the Big Crunch, we discard the spherical universe hypothesis too?
1604461031862.png

k>0 able us to find a solution for a dot = 0
 
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LCSphysicist said:
It is said, until this chapter, that the implication of k>0 inevitably implies a stop in the Universe expansion, and eventually a Universe's contraction. But, as far as i know, the Big Crunch was already discarded

When you say "the Big Crunch was already discarded", do you mean somewhere earlier in Liddle's textbook? If so, where?

If all you mean is that the Big Crunch is not currently predicted to happen for our actual universe, that's true, but it's irrelevant to what Liddle is saying in the chapter you refer to. He is talking about possible models in general, not about the specific model that we use to describe our actual universe.

LCSphysicist said:
to discard the Big Crunch, we discard the spherical universe hypothesis too?

If there is zero cosmological constant, then it is true that the universe having a hyperspherical spatial geometry and the universe ending in a Big Crunch must go together.

If there is a positive cosmological constant (as we believe is the case in our actual universe), that is no longer true. It is possible for a universe with hyperspherical spatial geometry to not end in a Big Crunch.
 
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1. What is the Big Crunch theory?

The Big Crunch theory is a cosmological model that suggests the universe will eventually stop expanding and begin contracting, eventually collapsing in on itself in a "crunch" and possibly leading to a new Big Bang.

2. How does the Big Crunch theory relate to the shape of the universe?

The Big Crunch theory is closely linked to the shape of the universe, as it suggests that the universe has a closed shape, meaning it has a finite amount of space and will eventually collapse back in on itself.

3. Is the Big Crunch theory still widely accepted?

No, the Big Crunch theory is no longer widely accepted in the scientific community. Observations of the expansion of the universe have shown that it is actually accelerating, making a Big Crunch scenario less likely.

4. What evidence supports the idea of a Big Crunch?

There is currently no direct evidence to support the idea of a Big Crunch. However, some early observations of the cosmic microwave background radiation seemed to suggest a closed universe, which would support the Big Crunch theory. However, more recent observations have shown that the universe is likely flat or even open.

5. What are the implications of a Big Crunch for the fate of the universe?

If the Big Crunch theory were true, it would mean that the universe is finite and has a definite end. It would also suggest that the universe goes through cycles of expansion and contraction, potentially leading to an infinite number of Big Bangs and Big Crunches. However, as mentioned before, this theory is no longer widely accepted and more research is needed to determine the ultimate fate of the universe.

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