Q:

"universe" or "universes"?

These striking facts have led us to consider one or another variety of
  parallel universe.

Shouldn't the word "universe" have been used in the plural?

A:

Either singular or plural universe is acceptable here.
Note that the author is not talking about universes but about varieties. When we speak of a variety or kind or category we are talking about ways to divide a set or class of objects. 
The set or class may be referred to either by its set "name"—a singular attribute which is shared by all its members—or by its set "membership", a plural attribute which denotes all the members.
For instance:

A spaniel is one kind of dog. 
  A collie is another kind of dog.
  Spaniel and collie are kinds of dog - that is, categories of the set "dog".
  Spaniel and collie are kinds of dogs - that is, categories of the set of all dogs. 

