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This is what I understand of the multiverse of the string landscape: the "laws of physics" reside in a 100-dimensional string landscape, which has ~$10^{500}$ minima. Each of the minima corresponds to a different set of laws of physics. We live in a universe which has a field value $V > 0$, which is why we observe a positive cosmological constant. It's very likely that we are not at the global minimum in the landscape. So we can quantum tunnel to another minimum where the field value $V < 0$. In this case, dark energy reverses sign, and the universe starts contracting.

Since this is almost surely going to happen eventually, in the infinitely far future, our universe is also almost surely going to end in a Big Crunch.

Is this correct? It doesn't seem to mesh with Wikipedia's article on the timeline of the far future. If it is correct, why doesn't it mesh? If it's incorrect, why is it incorrect?

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    $\begingroup$ What has 100 dimensions? What field is $V$ the value of? $\endgroup$ – G. Smith Dec 27 '19 at 13:12
  • $\begingroup$ @G.Smith the landscape has 100 dimensions, $V$ is the inflaton field. $\endgroup$ – Allure Dec 27 '19 at 13:15
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I think I've found the answer: yes.

Quoting from the book Eternal Inflation by Sergei Winitzki, page 82, footnote 2:

Asymptotically flat $\Lambda = 0$ vacua cannot support tunneling; vacua with $\Lambda < 0$ will quickly collapse to a "big crunch" singularity.

Papers cited are Coleman and De Luccia (1980) and Abbott and Coleman (1985).

If our universe has $\Lambda > 0$, it can only tunnel to a universe with smaller $\Lambda$. If that $\Lambda$ is less than $0$, then it will collapse, and in the multiverse every universe that is born is fated to end in a Big Crunch. Italics on "that is born", because somewhere in spacetime, eternal inflation is still ongoing.

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    $\begingroup$ This is mainly correct. However, there are two details that one must keep in mind: 1. Tunneling is an extremely low-probability event, so most likely life and stars will die out before anyone can witness such an event. Nobody will ever see it. 2. There are always other pockets of the universe that are still created from vacuum with some values of $Lambda > 0$. They undergo Big Bang and so on. Tunneling to $Lambda < 0 $ and Big Crunch is not a collapse of the entire existing universe, only a collapse of a specific pocket universe. $\endgroup$ – winitzki Jan 31 '20 at 10:07
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    $\begingroup$ The Wikipedia article puts together various hypotheses from various sources. At the end of their timeline, there is a tunnling event, but in the middle of the timeline, there is a hypothetical Big Rip (which requires a model of inflation with the equation of state $w = -1.5$ that has never been confirmed by observational data). Keep in mind that the entire premise of the string theory landscape with various vacua is also a hypothesis that was never confirmed by observational data (and neither was the string theory itself). $\endgroup$ – winitzki Jan 31 '20 at 10:10
  • $\begingroup$ O.o the author of the book verified it's correct! Have you considered writing your own answer and I can delete this one? $\endgroup$ – Allure Jan 31 '20 at 12:55

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