While writing SOP the general requirement is to mention a maximum of 3 to 4 prof as a potential supervisor. Since I have a broad field of interest (Cosmology, GR, Hep-theory) many universities have like 6 to 7 prof working in my field of interest. I want my application to be considered by each of them, but I heard that my application is sent to only those profs whom I mention in SOP. So, should I name each prof in SOP or just mention my field of interest and graduate committee sends my application to potential supervisors. It will be very helpful if someone can give some info about how the graduate committee decides potential supervisors.