Is the LSP the Graviton in Particle Physics?

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AmagicalFishy
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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.