Reason #1: Many, many world class physicists have invested their careers exploring the mathematics of "String Theory". If there isn't a multiverse, their careers are a complete waste & their further promotion prospects are grim.
Reason#2: Many science fiction novels and movies depend on it; we must consider the invested hours of authors and readers.
And then there are some more sanguine reasons:
http://www.quantamagazine.org/are-there-reasons-to-believe-in-a-multiverse-20230517/
excerpt:
"(45:5
It is just reminding physicists [of] the scary part of doing physics, which is that it is a high-risk, high-reward game. And you could be going down a path which you think might be fruitful for many decades and discover that it’s a dead end. And you may not even know why it’s a dead end. So these are concepts in physics, which could have an impact on individuals deciding whether or not solving the cosmological constant problem — why is it so small — is compelling or not. But it hasn’t landed us on a solution. And just like the universe has certain limits, there’s an observable universe, and there’s a certain finite amount that can be discovered in the universe just because of the potentially finite lifetime, if it is. Similarly, all humans have finite life. And there may be a finite capacity to discover all of the laws of nature.
(46:57) I personally have not been completely sold on the multiverse as explanations for these things, but I think they are plausible...."
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