Wigner classfied elementary particle as unitary irreducible representations (UIR) of the Poincaré group.
Suppose the spacetime is curved with symmetries $G$. Should the elementary particles in this spacetime always be UIR of $G$?
Specifically: Our universe has a positive cosmological constant, so shouldn't we look for unitary irreducible representations of the de Sitter group (as the next best approximation)? Or given a Schwarzschild spacetime: Should the elementary particles in this spacetime be UIR of its symmetries?
(It is clear to me that in general spacetimes have no symmetries at all. I'm wondering why it is the Poincaré group that has physical significance for our elementary particles and not, say, the de Sitter group. Or why do we even believe that elementary particles are UIR of Poincaré even though realistic spacetime of our universe do not have Poincaré symmetries.)