Bert asks for Sheldon's help in a geology research project relating to dark matter. Sheldon secretly agrees, but is too embarrassed to admit he is working with rocks. Bert finds out about this and ends their partnership. After talking with Amy, Sheldon goes to apologize, only to find Leonard has taken his place. Meanwhile, Raj runs into Ruchi again and goes out with her, but she does not believe in romantic love. After Howard and Bernadette tell Raj that he can just have sex with Ruchi, he agrees to keep it casual.
Sheldon and Amy go on their honeymoon to New York City, starting with Legoland New York. Sheldon's insistence on scheduling their marital relations stresses Amy. He says he only does it to remind himself to be intimate with her. They compromise by letting him make a schedule without sharing it with her. Leonard and Penny discover Mr. Larry Fowler (Teller) in Sheldon and Amy's apartment hiding from his wife (Kathy Bates). Leonard notices parallels in his own marriage, which offends Penny. Leonard apologizes, and Penny convinces Mrs. Fowler to give her husband a break. When Mrs. Fowler wants to hang out with her regularly, Penny scares Larry out of the building. Raj instigates a Twitter feud with Neil deGrasse Tyson but is scared off when confronted over the phone. Neil then calls Bill Nye to scare him, too.
Sheldon and Amy's wedding day arrives, with many friends and family attending, including Amy's domineering mother (Kathy Bates) and quiet father (Teller); Sheldon's mother Mary, brother George, and sister Missy, who is pregnant with her second child and separated from her husband; and Mark Hamill, who replaces Wil Wheaton as officiant as a favor to Howard who returned his lost dog. Sheldon cannot get his bow-tie to be symmetrical and conversations with Amy and his mother give him an epiphany about superasymmetry. Sheldon and Amy, along with Leonard, get caught up figuring out the math of the theory during the wedding ceremony, making Hamill take Star Wars questions to stall for time. Penny retrieves the couple, who then decide that they have the rest of their lives to make science together. Amy and Sheldon then express their vows. Amy recites a set of heartfelt vows, leaving Sheldon initially at a loss for words, before he reciprocates her loving words. They are pronounced as husband and wife.
Keith Carradine has appeared in three episode as Penny's father, Wyatt, first in Season 4. Katey Sagal, who played the on-screen mother of Kaley Cuoco's character in the 2002-2005 sitcom 8 Simple Rules, has appeared as Penny's mother in one episode of The Big Bang Theory. Jack McBrayer has appeared in one episode of The Big Bang Theory as Penny's brother, Randall.
One of the recurring plot lines is the relationship between Leonard and Penny. Leonard becomes attracted to Penny in the pilot episode and his need to do favors for her is a frequent point of humor in the first season. Meanwhile, Penny dates a series of muscular, attractive, unintelligent, and insensitive jocks. Their first long-term relationship begins when Leonard returns from a three-month expedition to the North Pole in the season 3 premiere. However, when Leonard tells Penny that he loves her, she realizes she cannot say it back. Both Leonard and Penny go on to date other people; most notably with Leonard dating Raj's sister Priya for much of season 4. This relationship is jeopardized when Leonard comes to falsely believe that Raj has slept with Penny, and ultimately ends when Priya sleeps with a former boyfriend in "The Good Guy Fluctuation".
When Raj misses out on a job at the planetarium, his father says he has no confidence because Howard always makes fun of him. Raj distances himself from Howard and later gets the job. Howard is hurt by this (even after apologizing to him) and tries to make amends with Raj after his first performance at the planetarium but, when he sees him get a date, he leaves without speaking to him, thinking that the latter's life is better without him. Meanwhile, Sheldon and Amy try randomly dividing up wedding tasks, but they keep arguing. The only thing they can agree on is to get married, so they decide to just get married at City Hall. However, Sheldon decides that he wants a first dance with his new wife and they go home to plan their wedding.