August 18, 2014 12:00 PM

Last but not least, give it up for Mr. Carter,” Beyoncé said onstage Aug. 3 before Jay Z chimed in, “No. Last but not least, give it up for Mrs. Carter.” On that warm, starlit night in Pasadena, the couple channeled love-struck teens flirting to see who would hang up the phone first. In fact, since the start of their joint On the Run Tour on June 25, the notoriously private couple have indulged in unprecedented PDA. During their shows, concertgoers get a glimpse inside their 2008 wedding ceremony (the couple had never publicly shared photos) and their life with daughter Blue Ivy, 2. However, many have begun to wonder if such cozy images have become a front for a marriage in peril. “Word around the industry has been that things are rocky at home,” a music source who has worked with Jay Z tells PEOPLE. “If they split, no one would be surprised.”

Such speculation is nothing new. Since they began dating in 2002, the stars have battled talk of infidelity. “There has been tension between them for a while,” says a source close to Jay Z. “To be honest, I thought they were going to get divorced before Blue Ivy was born.” A main reason they have remained together, adds another source, is their daughter: “She is the centerpiece of their marriage.”

Nonetheless, cracks began to show in the past few months. There was the infamous video that leaked in May of Beyoncé’s sister Solange, 28, attacking Jay Z, 44, in an elevator following a Met Gala afterparty. The trio quickly tried to downplay the argument, releasing a joint statement and posting photos of a happy family reunion in New Orleans 12 days later. Interestingly, Beyoncé, 32, has seemingly fanned the rumors and kept the story in the public eye. On June 28 she debuted new lyrics to her song “Resentment” that appeared to reference her marriage and Jay Z’s reported philandering. And with the release of her “Flawless” remix with Nicki Minaj on Aug. 2, she put the Solange-Jay Z incident back in the headlines by adding the verse “Sometimes s— goes down when it’s a billion dollars on an elevator.”

Over the years the couple’s shared drive helped build an empire (see sidebar), but it could also prove to be their undoing. “Their day-to-day lives revolve around business,” says an industry insider. “The constant pressure has taken much of the romance out of their relationship.” While a source says they lead “separate lives” when in New York, on the road they are the vision of domestic bliss. Between tour stops they enjoy family outings to local sights, with the singer sharing idyllic snaps of their trips on Instagram. Until they make some kind of official announcement, only they know the full truth. (Reps for both did not comment when reached.) “I think people have an idea in their heads about entertainers … like their lives are so perfect,” Beyoncé said last year in her HBO special Beyoncé: Life Is But a Dream. “[But] it’s really hard to go through painful experiences when you are in the public eye.”

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