It's a March afternoon in Los Angeles, and Coldplay has just announced on a local radio station that the band will perform its first live show in a year and a half this evening at the tiny Troubadour, on Sunset Boulevard. Up until now the concert has been a "secret," meaning that only half the city knew about it. The 300 lucky souls who manage to get in the door--a group that will naturally include singer Chris Martin's wife, Gwyneth Paltrow, and, completely unnaturally, Don Johnson--will be the first to hear songs from Coldplay's long-anticipated new CD, "X&Y." But at the moment the band's racing through a sound check, and there are only two people in the audience: Coldplay's publicist, who's tapping out an apology on her BlackBerry to a prominent magazine editor who's irked he didn't know about the gig, and a NEWSWEEK reporter. "Hi," Martin says into the microphone, "thanks to both of you for coming. I don't know if you remember us. We used to be big."

Once "X&Y" arrives on June 7, big is going to seem awfully small. About 60 seconds into the opening track, "Square One," a rush of guitar transforms Coldplay into something that, for all its gifts, it has never been: a thunderous rock-and-roll band. It's a deep, propulsive riff--a far cry from the bewitching melodies that have become Coldplay's stock in trade--and it sets the tone for an album that is, to put it as simply as possible, huge. Martin has never been shy about his belief that he's in "the best band in the world," and "X&Y" is a conscious effort to seize that title by force. "You want to be able to hold your head up high in a room with McCartney and Bono. That's one of the main things that drives me," says the singer, 28. "Are we trying to get to the next level? Yes. We're trying to get to the very highest level. We want to be better than Mozart. That doesn't mean we are, but that's what we're trying for. To me, there's no point in trying for anything less."

Coldplay doesn't have a reputation for mind-blowing live shows--a major flaw in its resume--but the muscular tunes on "X&Y" should take care of that. It is an album of anthems, built to be heard at supersonic volumes in arenas with 20,000 people. And on song after song, it's the guitar that puts the band over the top, turning mid-tempo rockers ("White Shadows," "Talk") into five-alarm blazes and giving heft to the CD's two obviously-about-Gwyneth tracks, "What If" and "Fix You." Both are lovely, but "Fix You," which is slated to be the second single, is the band's most elementally moving song since their breakthrough hit "Yellow." A close reading ("Tears stream/ down your face/when you lose something you can't replace") suggests it may be about the death of Paltrow's father in 2002. Like many of Coldplay's best songs, it skates on the brink of sentimentality with every note but never tips over. At a recent taping of VH1's "Storytellers," Martin called it "probably the most important song we've ever written." He's right. It's Coldplay's "With or Without You."

The only thing missing from "X&Y" is a teensy bit of daring. With the exception of the operatic title track, there's nothing here to match the structural originality of "Politik" from their last CD. Bands like U2 have been able to shed their skin once they've explored a sound for all it could offer; Coldplay is early in its career, but it hasn't hinted at a similar capacity for reinvention. If the band still sounds like this in five years, it won't have the same impact. At the moment, though, Coldplay may be the only rock band on the planet, U2 excepted, capable of galvanizing a broad, multigenerational audience. Evolution can wait.

Martin is indisputably Coldplay's engine, but there are, of course, three other people in the band. A guitarist, a bassist and a drummer--the usual. But it's a safe bet that you don't have the slightest idea what their names are. This is probably true even if you own both of Coldplay's two previous CDs, 2000's "Parachutes" and 2002's "A Rush of Blood to the Head," which have sold a combined 20 million copies worldwide, and even if you've read other articles about the band in which they've been quoted. By name. At least one of the three men--the guitarist--thinks this is just fine.

"Nobody knows the other members of bands," he says an hour after sound check, stretching out his 6-foot-3 frame on a sofa in a cozy suite at L.A.'s Chateau Marmont. "Only the singer. Look at R.E.M. Which one's the guitarist? The only reason I know Peter Buck's name is because of that time he got mad on a plane. The only way I could do it"--and by "it" he means achieving the level of fame enjoyed by Martin, who is so famous that his infant daughter, Apple, is better known than the rest of Coldplay combined--"is by getting into some kind of trouble. It could only be infamy." This is, of course, preposterous. Guitarists, especially, are often just as renowned as the singer. What about Keith Richards? "Massive drug habit." Come on, he's not known only for his drug habit. "But if he didn't have one, would he be as famous?" OK, Jimmy Page? "Witchcraft." The Edge? "Mustache." He laughs. "And how many people know his real name? Dave Evans, or whatever it is?"

Singers, rock-historically, are helium balloons--and guitarists are the guys with the rope around their waist keeping everyone anchored to the ground. The great thing about dynamic duos is that if you hate one of them, you can love the other. Coldplay could be even more compelling, notorious or whatever if its guitarist wasn't so damn... quiet. Right, Chris? "People who say that are c---s," says Martin. "It's the quiet ones you have to watch. China's pretty quiet, but it's also very great. When we're all speaking Chinese in 20 years, people will say, 'Well, I didn't realize--they were awfully quiet.' And when our guitarist is etched in marble all across England, people will say the same thing." Not if they don't know what to call him. But the guitar work on "X&Y" is so essential that anonymity won't be an issue much longer for Jonny Buckland.

By the way, now that you know it, isn't that a great name for a guitarist?

One frigid February afternoon in Manhattan, the members of Coldplay gather in a mixing studio to finish work on "X&Y." Martin, who's clad in a black turtleneck and black slacks, has been a dad less than a year. Fatherhood, he says, "is f---ing amazing," and he insists he wasn't the least bit petrified the moment he learned he was about to become a parent. "Nobody's ready for anything," he says. "That's life. But we're talking about a thing in my life--my daughter--that is nothing but positive, that brings me nothing but happiness. I know I have to work hard. I know I can't quit the band now and become a crack addict. But there are bigger things to fear in life, you know? Going deaf. Having to sit through an Anthony Minghella film."

Lyrically, "X&Y" pulses with the anxiety of a man confronting the reality that life will inevitably snatch away the things most dear to him. "With every album we do, we're two years closer to death," Martin says with a grin. While he is happy to talk about fatherhood, he gets cagey when asked, point blank, if certain songs on "X&Y" are about his wife and child. "No, not really," he begins. Then his irritation rises. "I mean, I don't know. I don't give a f--- what they're about. They're about what they're about." His bandmates expect to face the same question ad nauseam. "We haven't practiced any responses--Britney Spears does that sort of thing," says bassist Guy Berryman, 27. "But if you listen to the lyrics, you can pretty well tell."

Domesticity isn't the only thing that's changed Coldplay over the past few years. It returned from its 2003 world tour a much different band than when it left. "A Rush of Blood" was a slow-building smash that peaked with its last single, the cascading, piano-driven "Clocks." "If we tried really hard, I'm sure we could've been even more ubiquitous," says drummer Will Champion, 27, laughing. "But we knew it was time to kind of go away for a bit." The band had to adjust to life as a mainstream cog, loved and loathed in equal measure. "We're not a cool band anymore like the Strokes or the White Stripes, and sometimes I feel insecure about that," says Berryman. "But only occasionally." Then his eyes gleam. "And we'll just see who's around the longest, eh?" Martin admits he winced when Radiohead's Thom Yorke, one of his heroes, labeled Coldplay "lifestyle music"--a dig at the band's universality in films, stores, airports and Mom's iPod. "We're like an eager dog just yapping around their heels, and they're trying to kick us away," he jokes. "It's like unrequited love. I'm in love with a lot of things. Some of those things love me back. And some of them don't--and one of them is Radiohead."

Trying to raise its game with "X&Y," Coldplay got off to a sluggish start. (Martin will disclose only two things about the album title: that it refers to the "tension of opposites" and that it was chosen over "The Outstanding Pectorals of Guy Berryman.") The guys went into the studio less than two weeks after the end of their tour and were still, according to Buckland, a bit too high on the fumes of their own awesomeness. "You get off tour and you think you're the greatest band ever because you've just been playing the same thing over and over, so you're really good at it," says the guitarist, 27. "And then you go into the studio, still thinking you're the greatest ever. So you think--or at least I certainly thought that everything I was writing was great. Then you play it back and you slowly realize, 'Actually, that's... that's not very good'." After a break to recharge, the guys gathered in a dingy north London rehearsal space, where they spent weeks jamming until things started to click.

At the mixing studio this evening, Coldplay is finally nearing the finish line with "X&Y." As Buckland and Champion muck around on their laptops in the next room, Martin and Berryman scrutinize the latest pass at "Fix You." As the song booms through the speakers, Martin yells out instructions to the engineer. "The first line of the chorus is a bit too... wet. Also, the bass needs to be just a little crisper. It's meant to sound New Order-ish." Berryman nods as the engineer fiddles with a dial. There. Perfect. "I can't listen to it anymore," says the singer. "There comes a point when you've heard something 8 million times and you've got to let it go." It's late and the band is craving dinner. Martin gets up to leave and grabs his jacket. But if he doesn't listen to a song more than 8 million times, are we going to? He puts his jacket back down. "OK, one more time."