There's a nice mathematical explanation to the existence of antiparticles.It involves involuted associative algebras.For example,the complex numbers form such an algebra and the complex scalar field,which is an element of such an algebra,describes,after quantization both particles & antiparticles.
See if the electromagnetic field [itex] A_{\mu}(x) [/itex] and the gravity field (well,either one of the 3 possible fields describing it) could form such an algebra.
Daniel.
