In the Marvel Cinematic Universe, it is heavily implied that Howard Stark knew that Tony Stark was his son. While there is no explicit confirmation of this fact in the movies, there are several pieces of evidence that support this theory.
One of the most compelling pieces of evidence is the fact that Howard Stark created a special element that he knew only Tony would be able to synthesize. In the movie “Iron Man 2,” Tony discovers a hidden message from his father in a model of the 1974 Stark Expo. The message contains a set of instructions for creating a new element that can power the Arc Reactor in Tony’s chest, which is keeping him alive. The instructions are coded in a way that only Tony, who has inherited his father’s genius-level intellect, would be able to decipher.
This suggests that Howard Stark knew that Tony was his son and was planning ahead for the day when Tony would need his help. It also implies that Howard had a level of confidence in Tony’s abilities and intelligence that could only come from a father who knows his son well.
Another piece of evidence is the way that Howard speaks about Tony in “Captain America: The First Avenger.” In the movie, Howard is shown to be working on the development of the Super Soldier Serum that will eventually turn Steve Rogers into Captain America. During a conversation with Steve, Howard mentions that he has a son who is about Steve’s age and is interested in science and engineering. He also mentions that his son is a bit of a handful and has a tendency to get into trouble.
While Howard does not mention Tony by name, it is strongly implied that he is referring to him. This suggests that Howard knew about Tony’s interests and personality, and was proud of his son despite his flaws.
Finally, there is the fact that Howard kept a detailed record of his work and personal life, which Tony discovers in “Captain America: Civil War.” In the movie, Tony watches a holographic message from his father that was recorded shortly before Howard’s death. In the message, Howard speaks directly to Tony and tells him that he is proud of him and loves him.
This scene implies that Howard knew that Tony was his son and had a close relationship with him, despite their complicated history. It also suggests that Howard was planning ahead for the day when Tony would have to take over his legacy, and was trying to prepare him for the challenges that lay ahead.
In conclusion, while there is no explicit confirmation in the Marvel Cinematic Universe that Howard Stark knew that Tony was his son, there are several pieces of evidence that strongly suggest this is the case. Howard’s creation of a special element that only Tony could synthesize, his comments about his son’s interests and personality, and his holographic message to Tony all imply that Howard knew about Tony’s true identity and had a close relationship with him.