When you open the PDF inline in browser you get a "page expired" when you go back?
Where do you open the document from? Is it from inside a document library or from custom code?
I am asking this because getting a "page expired" is connected to doing a POST request (postback) and accessing from a document library is a GET request.
Caching can also be an issue, but again only in combination with a POST. You can examine what output cache profile you are using (an easy way to do this is by checking the Cache-Control header in the response header of the page using a program like Fiddler