impossible to make really infinite geometry.
make ground plane small enough to cover all areas where shadowcasting will occur and assign useBackground shader. Next find which works better:
A) make imagePlane and assign any suitable env texture. make imagePlane.depth value near farClipping value of camera.
create large enough sphere and apply incandescent shader with spherically projected texture e.g. ramp.
Ground plane will catch shadows, A or B will show infinite environment. Fake.