A startup search engine launched Monday, Cuil, hopes to prove that its search technology is cooler than that of the reigning king of search, Google. Cuil’s creators — former Google search architect Anna Patterson; her husband Tom Costello, a former researcher and developer at Stanford University and IBM; and Russell Power, another former Google executive — claim they have pioneered a new take on the search game, combining the largest index of Web pages — 120 billion — with a content-based relevance methodology.