Is the LSP the Graviton in Particle Physics?

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Hey, guys.

I'm going to start off by saying I know near nothing regarding physics and don't claim to be more than completely ignorant in anything passed the fields considered pre-calculus. I have a huge interest in particle physics, though—and have decided to take a more academically rigerous path to actually learn physics, in depth.

Anyway, my interest in the field compels me to do things like download lectures, and while I can only comprehend about 20% of the things that are over-simplified, I enjoy listening to them anyway (and try to grasp onto the few concepts that I can).

So, that is where this question is coming from. . .

Is it possible that the LSP is the graviton? If everything were to decay down to the LSP, perhaps the graviton doesn't have a super-symmetric particle—and is like the "0" in numbers (with no opposite)?

Or is that an idea that is physically impossible?
 
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When you talk about the LSP, you implicitly are talking about particles with mass. The graviton is massless and therefore is not a part of that.

Now, it turns out that the superpartner of the graviton (the gravitino), does usually have mass and can in some models be the LSP.
 
I seem to notice a buildup of papers like this: Detecting single gravitons with quantum sensing. (OK, old one.) Toward graviton detection via photon-graviton quantum state conversion Is this akin to “we’re soon gonna put string theory to the test”, or are these legit? Mind, I’m not expecting anyone to read the papers and explain them to me, but if one of you educated people already have an opinion I’d like to hear it. If not please ignore me. EDIT: I strongly suspect it’s bunk but...

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