Radiation bounce from the Lee-Wick construction?

It was recently realized that matter modeled by the scalar field sector of the Lee-Wick standard model yields, in the context of a homogeneous and isotropic cosmological background, a bouncing cosmology. However, bouncing cosmologies induced by pressureless matter are in general unstable to the addition of relativistic matter (i.e. radiation). Here we study the possibility of obtaining a bouncing cosmology if we add not only radiation, but also its Lee-Wick partner, to the matter sector. We find that, in general, no bounce occurs. The only way to obtain a bounce is to choose initial conditions with very special phases of the radiation field and its Lee-Wick partner.