Can dark matter actually be gravitational radiation?

Question

It seems to exist like only space distortion, and it seems to move just like radiation (specially when galaxy clusters collide, dark matter goes trough unaffected just like some type of radiation).

It is like dark matter is just ripples in space. Like, small dents in a car's metal, dark matter can just be a dent in space (a local deformity of space) that exists there, instead of a WIMP.

Have we ruled this hypothesis? That dark matter is not a particle but a localized space deformation that exists by default, without the need of particles to justify that deformation?

The same way a car dent can exist by itself, could a space dent (deformity) just exist without any particles in that region whose mass justifies the dent? i.e. Can space be bent naturally in a given region without having to fill that region with massive particles? If so, these bent but mass-free regions could be dark matter. They hold energy and create gravity by being bent, but do not have massive particles there, all their energy is stored as the bent itself and manifests as gravity.

Answer 1

It does not move at all like radiation of any kind. If it did, it would radiate away from galaxies into intergalactic space, where it wouldn’t provide the extra invisible mass that galactic rotation curves indicate galaxies have, gravitationally bound in a halo.

And if the universe was filled with all this extra “dark radiation”, the anisotropies of the cosmic microwave background would not match models with dark matter. Matter and radiation have very different energy-momentum tensors, and thus affect the expansion of the universe in different ways. (Also, the energy-momentum of gravitational radiation is a subtle subject, but it definitely isn’t like that of matter.)

So, yes, this hypothesis has been ruled out. Actually, I don’t think it was ever considered.