What is space became a conductor?

What would happen if the space between the sun and the earth suddenly became conductive? I'm really bad with this kind of stuff (thermodynamics?) so I don't know how to specify what I mean but let's say, for example, that the space suddenly became filled with an atmosphere similar to Earth's. How would that change the solar radiation that reaches us? How about if it became as conductive as, I don't know, copper?