When I was a child I read a book of short stories, I think it may have been Ray Bradbury. Anyway a cosmonaut leaves earth at near-light speeds and returns what

When I was a child I read a book of short stories, I think it may have been Ray Bradbury. Anyway a cosmonaut leaves earth at near-light speeds and returns what are a few months to him, I dont remember how many years had passed on earth. The world was covered in green goo and the only people left were Americans and Russians living in submarines and still trying to kill each other with biological warfare. I believe anyway, this was about 25 years ago. It made me very afraid of all arms races. Does anyone happen to know the name of the author/book/story?