It is always possible to publish without affiliation, but I'd recommend you try and "get" some affiliation nevertheless. Many universities have interest groups,

It is always possible to publish without affiliation, but I'd recommend you try and "get" some affiliation nevertheless. Many universities have interest groups, reading groups, loose projects, etc., that in principle anyone can join, and in most cases all you need is one project leader or professor interested in your publications who allows you to mention the affiliation. For instance, at our institute we have the status of a collaborating member, which includes anyone from the outside who works together with someone from the institute on a project. There are restrictions of our funding agencies of what we can count as a publication of our institute, of course, for that you need to be an integrated member, but that's another issue. At least that's how it works in many places in Europe, I imagine some places in the US have stricter conditions, especially the top universities. Anyway, contact some people at universities and see if they are interested. That's my advice - assuming that your planned research and publications are of high quality. If not, you're going to have a hard time convincing anyone, of course.