Peter Arndt was Jessica Arndt's husband.
Arndt was born on April 2, 1971, in Philadelphia. (“Many Happy Returns”)
Peter and Jessica eventually married. While at a bar in New York, he unknowingly met with Reese while waiting for Jessica. Excited to hear that Reese was from the same hometown as his wife, Peter waited for Jessica to arrive, but Reese left before he could "introduce" her to him. (“Blue Code”)
Jessica mentions that her marriage with Peter is fine when talking with Reese on the phone, while he is on a mission in Morocco. (“Matsya Nyaya”)
This was revealed to be false however, as Peter was abusive to Jessica as he frequently twisted her wrists and hit her. This abuse would cause Jessica's social security number to appear repeatedly on the Machine's irrelevant list. (“Ghosts”) Eventually, Peter accidentally pushed Jessica over, causing blunt force trauma to her head, killing her. Rather than call 911, he staged a car accident which later was determined to have caused her death. (“Many Happy Returns”).
In February, Peter would continue about his life but with a brace for his leg. One night, he came home to find Reese watching his wedding video, suspecting he was an employee of a loan shark he owed a large sum of money. Realizing he was of importance to Jessica seeking to hurt him, he grabbed a fireplace poker and tried in vain to fight Reese.