**Turning gravity upside down**

The new theory that challenges our understanding of what it is and how it works.

Back in the 1930s, theoretical physicist Wolfgang Pauli and physicist Markus Fierz came up with a radical idea.

What if gravity had a mass? And what if there was a theoretical particle called a massive graviton?

Could this simple theory help to explain one of the universe’s biggest mysteries – why gravity, in many instances, simply doesn’t act as Einstein’s and Newton’s theories suggest it should?

The answer, at the time, was: maybe. However, their theory never really caught on. By the 1970s, physicists had found numerous problems with it.

But it turns out that this idea wasn’t dead – just waiting to be revived by new thinking and new frontiers in cosmological and theoretical physics.

In short, it was waiting for the de Rham-Gabadadze-Tolley (dRGT) theory, the result of work by theoretical physicist Professor Claudia de Rham and theoretical cosmologist Professor Andrew Tolley at Imperial, and Professor Gregory Gabadadze at New York University.

How can we explain the things that Einstein’s theory can’t explain?

“The beautiful thing about Einstein’s theory of general relativity is that the red flags are built in – we know that, at some point, it will stop working,” says De Rham.

“It tells us exactly when it’s breaking down, and when new physics is needed. That doesn’t happen very often in science.

"So, our big question is: ‘How can we explain the things that Einstein’s theory can’t explain?’”

And there is a lot to explain. The more we discover about our universe, the more it has become clear that neither Einstein’s or Newton’s theories explain everything we need to know about how it began, how it works and how it’s behaving now.

Newton’s theory, for example, breaks down in areas with a very strong gravitational field, such as black holes. And, as recently as 2015, the discovery of gravitational waves has opened up a whole new world of questions and anomalies around gravity.

Hence, the dRGT theory, which, in its simplest form, posits a theoretical particle called a graviton, that has a mass.

It aims to explain one of the biggest problems confounding cosmologists and physicists today: our universe is expanding, much faster than predicted, and galaxies are moving away from each other, faster and faster.

This is precisely where new physics is needed to explain that accelerated expansion. In response, cosmologists have hypothesised ‘dark components’: fluids or substances that affect gravity, but the actual identity of which is unknown.

These could explain why galaxies are receding from each other, despite having an attractive force between them.

But then you come up against another big issue: the so-called cosmological constant problem.

Around 22 per cent of these dark components is dark matter, which behaves more or less the same from a gravitational point of view as normal matter.

But 74 per cent is ‘dark energy’, which, as Tolley points out, is “really just a name for ‘lack of knowledge”.

Nobody has been able to actually find any dark energy. And when you try to calculate the amount of theoretical dark energy in the universe according to Einstein’s theory, it ends up being far more than what has been observed – around 10120, according to some expectations.

"If we use general relativity in order to describe this cosmological expansion, it breaks down, at cosmological scales,” says Tolley.

“General relativity works at smaller scales – I mean galactic – but not on this scale.”

A new approach was needed, and De Rham and Tolley were ideally placed to find a new way in.

They first met in Cambridge, where they were both independently working on the concept of ‘braneworlds’ – the theoretical existence of extra dimensions, and ‘branes’, membranes or surfaces that exist in these dimensions.

And their familiarity with these concepts helped them find a new way to think about massive gravity.

“When we started, there were many very famous physicists who had proved that it was simply not possible for gravity to have a mass,” says De Rham.

“There were lots of no-goes. So, the way we dealt with that was to initially work with extra dimensions, in addition to the usual four.

"We looked into the extradimensional models that we came up with – and then we realised that the way we were evading the no-goes had nothing to do with working in extra dimensions.

"We could evade them in four dimensions as well, in ways that hadn’t been accounted for. Working in the extradimensional gave us guidance in how to deal with the problem in a much simpler way that we had anticipated.”

According to Einstein’s theory of relativity, gravity is a distortion of spacetime. An object (such as a planet) has a mass, which creates a gravitational field that can be warped and changed.

We still get papers saying it's either wrong, not new or useless. It's not the ultimate theory, but it remains the best we've got

“The simplest way to change any force at large distances is to give a mass to the particle that propagates that force,” says Tolley.

“The more mass you give to the particle that propagates the force, the harder it is for it to propagate over large distances.

In practice, the force decays exponentially through what’s called Yukawa suppression. This means gravity becomes weaker over large distances.”

So, when gravity is given a mass, it can explain the universe’s acceleration without the need for dark energy.

They’re at pains to point out that not everybody agrees with them.

“We still get papers saying it’s either wrong, not new or useless – or even all three at the same time,” says De Rham, co-recipient of the Adams Prize for contributions to mathematics in 2018, and Blavatnik Physical Sciences and Engineering finalist for the inaugural Blavatnik Awards in the UK.

“It’s been killed so many times! And just like general relativity, we know it will fail at some point, but it's still a very good description of what's going on.

"Our theory is not the ultimate theory. No one ever thought it would be the ultimate theory. But it's still the best we have got.”

We are getting closer and closer to having a completion of what the graviton particle content is as a whole, even if we can’t observe it

And it’s opened the door to even more questions and research, alongside the Laser Interferometer Gravitational-Wave Observatory’s detection of gravitational waves in 2015.

“That’s surely the discovery of our scientific lifetime,” says De Rham.

“Cosmology is the new way of doing particle physics from phenomenology, because it's getting harder and harder to crank up energies on Earth in accelerators.

"More and more, it's giving us the opportunity to test particle physics not in the lab, but by just observing.”

So, does this mean they are close to the fabled Theory of Everything? Not quite, they emphasise, but they’re moving in the right direction.

“By understanding how gravity interacts with other fields and how other fields react to it, we are getting closer and closer to having a completion of what the graviton particle content is as a whole, even if we can’t observe it,” says De Rham.

“Gravity interacts with everything, and as gravitational waves propagate, we will get signatures of their interactions with everything. It’s the start of something.

"We don’t yet know where that will go. And that’s the exciting part.”

*Imperial* is the magazine for the Imperial community. It delivers expert comment, insight and context from – and on – the College’s engineers, mathematicians, scientists, medics, coders and leaders, as well as stories about student life and alumni experiences.

This story was published originally in Imperial 47/Winter 2019-20.