My layperson understanding is that GR specifies that energy/mass-momemtum influences space-time curvature which then produces gravity (as particles travelling along straight lines in the curved space). That would imply that fermions are therefore the force carriers for gravity, not a hypothetical new boson.
> My layperson understanding is that GR specifies that energy/mass-momemtum influences space-time curvature which then produces gravity (as particles travelling along straight lines in the curved space).
That's correct. However...
> That would imply that fermions are therefore the force carriers for gravity, not a hypothetical new boson.
That's wrong. Energy/mass-momentum (which can, as hughesjj points out, be bosons or fermions or both) is the source of gravity. The source is not the same as the "force carrier". (For example, in electromagnetism the source is charge/current, but the force carrier is the photon.)
In GR, gravity has no "force carrier" because it is not a force. In the simplest quantum model that has a "force carrier" for gravity, the quantum field theory of a massless spin-2 field, the "force carrier" is the massless spin-2 graviton, which is not the same as any source that occurs in ordinary matter.
Well, bosons also have mass and can distort space. Theoretically even the (rest-)massless photon distorts spacetime, think it's called a kugelblitz. Also how would fermions be the force carriers if they don't physically move through space themselves to interact with far away fermions, ex gravitational waves? Unless you're advocating for a relational model of space which hey I'm all for but introduces other issues afaik
