Robert Downey Jr.'s Wife Woke Him from Nightmare About His Kittens to Break His Oscar News (Exclusive)  

Robert Downey Jr. is glad not all dreams come true.

The Oppenheimer star, 57, tells PEOPLE he was woken from a strange dream by his wife, producer Susan Downey, when he learned he had been nominated for an Oscar.

“I was having this nightmare that the kittens [Willow and Winifred] had taken one of my Nicorette wrappers, and I was going to get in trouble," says Downey, who sat down with costars Cillian Murphy and Emily Blunt to discuss the film and their friendship for PEOPLE's annual Oscar portfolio.

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories. 

Downey said he celebrated the good news with his wife and later Facetimed with Blunt. While he is thrilled to get the Oscar nomination, he says the true prize has been spending time with the film's cast.

"The reward was the experience. There is a bond and we have just huge respect for each other," Downey says of his costars.

In the Christopher Nolan-directed film, nominated for Best Picture, Murphy plays physicist J. Robert Oppenheimer, the so-called “father of the atomic bomb.” Blunt plays his wife, Kitty and Downey portrays Lewis Strauss, chairman of the Atomic Energy Commission.

Blunt, who is nominated for Best Supporting Actress, says having her costars by her side makes all the difference.

"I'm just happy we have each other. I feel like we've been such a little gang of this Oppenheimer ride, which seems to be forever lasting and extends beyond what any of us dreamt of."

The 96th Academy Awards, hosted by Jimmy Kimmel, will air live on Sunday, March 10, from the Dolby Theatre in Hollywood, California, beginning at 7 p.m. ET.