According to the script, Eve is 2000 years old and was the druid matriarch of a Celtic tribe. Adam is 500 to 600 years old. Jim Jarmusch decided that Adam and Eve would be aware of each other's true age so he argued they have no reason to state it in the film, but simply informed the actors of the age of the characters. In an extended version of the nude scene, shown in the DVD special features, Adam & Eve do talk about her druidic connections.
The white dwarf Eve mentions to Adam while driving across the city is the star called BPM 37093, also known as Lucy (named after The Beatles song Lucy in the Sky with Diamonds). Its nucleus is in a cooling down process, which makes the star core pulsate like a giant gong.
Contrary to most viewers' assumption, Jim Jarmusch did not name the two main characters directly after the Adam and Eve of the Bible; rather, he was referring to Mark Twain's satirical work "The Diaries of Adam and Eve," which has rarely been published in its complete form. Jarmusch told a Hollywood Reporter interviewer that "it wasn't until shooting the film that I realized everyone's first impression will be the biblical reference. Whoops. It's too late now. What can I do?" Twain's is one of the faces visible on Adam's wall of framed portraits in the movie.
Eve books a flight for herself and Adam under the names "Daisy Buchanan" and "Stephen Dedalus," main characters in F. Scott Fitzgerald's "The Great Gatsby" and James Joyce's "A Portrait of the Artist as a Young Man," respectively. Stephen Dedalus also appears as the sidekick in Joyce's "Ulysses." In Joyce's final novel "Finnegans Wake," there is a famous recurring poem with the line "riverrun past eve and adam."
There's a bar in Delray (Detroit) that they filmed some outside shots at. The bar was called "Ideal" and had been closed since 1986. The old man who owned the bar had to purchase the house next door in order to have access to the cement stairway between the buildings to get to the outside basement level of the bar. The old man told everyone on the cast and crew who would listen how it took him so long to purchase the bar and to talk the old lady that owned the house to sell to him although he didn't want the house (he only wanted the cement staircase that led to the basement level). Shortly after the filming at the bar (which took place in late July 2012) the old man torched the house next door for the insurance money.
Although Jim Jarmusch wanted to shoot this movie on film and has a general distaste for digital cinematography, he had to use the Arri Alexa for budgetary reasons. He managed to work with low lighting and specific lenses in order to come up with a look he found acceptable enough to work for him.
The film shares its title with a 1964 Dave Wallis science-fiction novel which was considered as a film project for The Rolling Stones and would have been directed by Nicholas Ray, who mentored Jim Jarmusch in the 1970s when he was a graduate student at NYU.