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London’s stadium summer is about to begin and Muse intend to kick off proceedings with a deafening bang. I wouldn’t want to be Rihanna, Green Day, The Killers or Robbie Williams and have to follow the grand-scale spectacle that the Devon trio are promising at the Emirates Stadium this weekend.

For Muse are the biggest band in the world right now — perhaps not quite the most commercially popular, but certainly the largest in terms of the size of their concert productions, the galaxy-crushing rock of their six albums and their ambition to make audiences feel like the world is coming to an end every time they play.

After a lengthy arena tour last autumn and a slot at the Olympics closing ceremony concert last summer (playing their menacing, utterly bonkers official anthem, Survival) these beasts that walk the earth are back in their natural habitat. If you believe their 34-year-old singer and guitarist, Matt Bellamy, it could be the last time.

“As a band I think we’re at the moment of collapse,” he tells me. “We’re at the point of being forced to go back to the basics.”

This isn’t the first time he has threatened to break out the acoustic guitars and start making campfire music, of course. But there’s something about the way he speaks of this stadium tour that suggests Muse are about to reach their peak.

“This is going to be our Zoo TV,” he says, referring to U2’s extravagant early Nineties tour featuring suspended Trabant cars, endless flashing TV sets, Bono’s turn as The Fly and live satellite link-ups with Sarajevo. “This will be the tour when everyone goes, ‘You’ve gone too far, you shouldn’t have done that’. I’m pretty confident about that, and I’m glad. It’s a totally different show from the arena tour. I feel like we’ve scaled up and scaled up every time and I’m very confident that this is as far as you can go.”

I’m not sure whether to believe him when I ask what we can expect from the show. If he’s telling the truth, it will certainly live long in the memory. “We’ve got a 20ft robot called Charles who’s going to go around the stadium barking at everyone, then he’s going to go outside and cause traffic jams. We’ve got an actor playing a banker who’s going to have a banking crisis on stage as we do our own version of quantitative easing, and spray the audience with millions of euros. We might have a businesswoman drinking petrol. The stage is basically a giant futuristic industrial power station polluting the world.”

The set-up is inspired by the main theme of their most recent album, The 2nd Law. It’s named after the second law of thermodynamics, which is not easy to grasp but which is partly explained by a sampled female voice on the song Unsustainable: “The fundamental laws of thermodynamics will place fixed limits on technological innovation and human advancement. In an isolated system the entropy can only increase. A species set on endless growth is unsustainable.”

So it’s the story of the planet, and the financial system, although Bellamy insists that unlike U2, his band aren’t out to preach. “There have always been elements of message in our music, but we don’t make music for the message,” he says. “I don’t think we’re trying to take a stance on anything. I think we’re trying to honestly express some of the confusion of what it is to live in these times. I’m yet to get up on a pedestal and say, ‘This is what needs to happen’.”

He’s aware, too, that the theme also reflects his band’s exponential growth from easily dismissed Radiohead and Jeff Buckley copyists around the time of their 1999 debut, Showbiz, to uniquely overblown space rockers adored for putting on a show like no one else.

He sounds like a reluctant environmentalist. “We all want to escape off the planet in spaceships and live like Star Trek but that appears not to be happening. Instead we’re being told we’ve got to go backwards. That’s a depressing thought. So as much as I love the idea of a sustainable future and all the environmental stuff, there is still a part of me that just wants to go [blows giant raspberry] f*** it all, and push for progress.”

Even so, he still promises a quieter future. I mention that the last time I saw Muse live was at a War Child charity show in the relatively minuscule space of the Shepherd’s Bush Empire in February.

“That was a totally different feeling, although we were still doing the big rock songs. I loved it so much that I think on the next tour, every city we go to, I wouldn’t mind pulling a Prince. Do the arena gig and then show up in some little club late at night.”

It might be the one area where a band that could be said to have done it all still have things to do. “We have work to do with intimacy, connection, stripped-down organic stuff and all those warm fuzzy words. There’s definitely something in that department that we want to explore.”

It’s understandable that the trio might want to calm down a bit as they approach elder statesmanship. Bellamy and bassist Chris Wolstenholme have young families. Bellamy’s son Bing with his wife, Hollywood actress Kate Hudson, is almost two and fascinated by the work of Muse drummer Dom Howard. “Bing is obsessed with drumming. He loves hitting things.”

Wolstenholme has also reached a more serene space after going through rehab in 2009, having spent most of the band’s existence as an alcoholic. He wrote and sang two songs on The 2nd Law, Save Me and Liquid State, the latter containing the lyrics: “The iniquity has died inside and left a scar/I’m all red and done/Bring me peace and wash away my dirt.”

“On this last tour it’s like he’s a different person,” says Bellamy. “He’s totally sunny now and it reminds us of when we first got together. He’s got that youthful energy back. It makes it a lot more fun being on the road. There’s no one who’s down and wants to go home.”

He says the band would have split altogether before they’d have kicked Wolstenholme out. It’s easy to forget, as they stand astride laser cannons and conduct the most apocalyptic rock show in existence, that Muse are just three school friends from Teignmouth. If they do make the long-threatened return to their roots after one last stadium blowout, they’ll have earned a bit of peace and quiet.

Muse play Emirates Stadium, N5, 08444 999 990, muse.mu, Sat May 25 and Sun May 26.