# Interview with Claudia de Rham

*For one week in November, Geneva hosted the 18th edition of the annual Wright Colloquium. This year's theme was "Gravity" The Universal Attraction" and gathered researchers and thinkers to present their research and share some of the questions that intrigue them while showing off the most fascinating data that could help us understand this so fundamental and yet elusive force.*

*Professor Claudia de Rham discussed about "The Dark Side of the Universe". A faculty member at Imperial College London, de Rham grapples with some of the most fundamental questions at the intersection of gravity, cosmology and particle physics. In her talk, she invited the audience on a journey to the outskirts of the observable Universe in a quest to understand the behaviour of gravitation and how it is linked with the so-called Dark Energy.*

*We met de Rham before her talk and discussed about the nature of gravity, her work on massive gravity and possible observables coming from gravitational waves. How can a new theory of gravity help us tackle the dark-energy content and what can be learned from collider experiments? Finally, we discuss with her about the need for a paradigm-shift in science communication.*

**What motivated you to become a cosmologist?**

As a child, I enjoyed staring at the starry sky! In fact, like perhaps many kids, I was dreaming off becoming an astronaut. Later, as an undergraduate student, I had the opportunity to do an internship in NASA’s Jet Propulsion Laboratory. My project was to study the correlation between the magnetic and gravitational fields of Mars and involved a lot of data analysis. This helped me to realise that I was interested in more fundamental questions. Questions related to the first principles and basic laws that describe our universe. This is when I have decided to focus on theoretical physics.

In that sense, cosmology has been the obvious choice since it offers the opportunity to explore nature at its most fundamental level while keeping a sort of “connection” with the sky! Through cosmology we try to answer the most fundamental questions about our own existence and the origins of the universe.

**What do you see today as the main challenges for cosmology? **

A key challenge comes with the new observational data allowing to look much further and at different epochs of our Universe. More data means also more effort to interpret them, thus calling for theoretical developments.

Moreover, when designing new missions we also need to think the type of data needed to verify our theories or understand where to search next. From a theoretical perspective, I think that there is still a lot of work needed on the foundations of theoretical cosmology. Pioneers, like Steven Hawking, Roger Penrose, Steven Weinberg, Tom Kibble formulated the basis of our current understanding back in the 1960s and set the framework for further theoretical and experimental exploration. They were amazing in communicating their ideas to a larger group of people creating a whole new community. This is their legacy. The community that inherited their ideas is today the main driving force of our field.

**You have recently received the Blavatnik award for your work in massive gravity. What’s the key concept behind this idea? **

Massive gravity is exactly what you think when you hear these two words! Some of the particle carriers of forces in the Standard Model have a mass, like the W and Z bosons that carry the electroweak force. Today we believe that the photon is massless though there are some theoretical ideas that it could also have a mass and certain constraints have been placed on its value.

Massive gravity introduces a similar concept for the graviton - or any spin-2 particle - that is the carrier of the gravitational force. Today, we believe that like photons, such particles, if they exist, are massless. The theory of massive gravity though suggests that they have a certain mass and succeeds to introduce it without violating other theoretical or experimental constraints.

The possibility of a massive graviton is not something new. In fact throughout the 20th century there were efforts to incorporate this in GR but a number of issues arised. These problems are similar to what happens when you give a mass to the photon; as soon it gets mass it can’t travel anymore at the speed of light while excitations along its travel path introduce an extra degree of freedom in the electromagnetic field.

Similarly, adding mass to the carrier of the gravitational force would add additional polarizations in the gravitational waves as they travel in spacetime. This effect was understood already in the 30s when Wolfgang Pauli and Markus Fierz developed a theory of a massive spin-2 field propagating on a flat spacetime background. Moreover, it was later understood that giving a mass to the graviton adds extra degrees of freedom that makes the theory very unstable. Massive gravity comes with a so-called “ghost”; an instability that cannot be controlled and to which every particle would decay very rapidly. This of course can’t be the case and for decades people thought that a massive graviton - any spin 2 particle that carries gravity - is excluded.

This was also our mindset and within the community we were exploring different complementary options. I started playing with a specific model and during cosmo 2008 at CERN I realized that Gregory Gabadadze had come up with precisely the same model. We started discussing and that’s how we started our collaboration!

We knew that our model was not fully consistent and required further completion. For example, we could see that it violated the existing no-go theorems for massive gravity, which indicated that there could actually be a loophole behind these long standing arguments against massive gravity. To solve that we started exploring the maths behind the theorem (or performing a more careful constraint analysis) and soon discovered how the no-go theorems could in fact be evaded and how to allow the graviton to have a mass. So together with Gabadadze and Andrew Tolley we developed a fully consistent theory of massive gravity accommodating a massive graviton.

It will most probably not be the final description of what is going on but it certainly provides a framework with which we can explore alternative theories of gravity, at least at the largest cosmological scales.

**In 2010 a breakthrough was achieved when de Rham, Gabadadze, and Tolley constructed, to all orders, a theory of massive gravity with coefficients tuned to avoid the Boulware-Deser ghost by packaging all ghostly (i.e., higher-derivative) operators into total derivatives which do not contribute to the equations of motion. The absence of ghost was proven perturbatively and to all orders in some dimensions. The complete absence of the Boulware-Deser ghost, to all orders in general dimensions was subsequently proven by Fawad Hassan and Rachel Rosen. **

**Which challenges does the theory of massive gravity address? **

This boils down to the so-called cosmological constant problem. The cosmological constant, that is linked to the energy of the vacuum, seems a very natural candidate for dark energy. Therefore, you may ask why not to keep only that as a simple and elegant solution to the dark energy problem and assume that the vacuum energy is responsible for the observed expansion of the universe?

Well, then you confront the real problem because if you try to calculate how much each particle contributes to the vacuum energy with the known laws of particle physics, you end up with a very large number which is 120 orders of magnitude higher than what we observe. This is perhaps a strong statement as it assumes that there are particles contributing to the vacuum energy all the way up to the Planck scale (or it assumes a cutoff of the order of the Planck scale). In my view this is not necessarily the case. However, even restricting ourselves to known particles, like the recently discovered Higgs boson, with a mass of 125 GeV, would give us a discrepancy of 56-57 orders of magnitude with observations. That’s the cosmological constant problem.

The motivation for massive gravity is to get the best of both worlds: you say that the vacuum energy is responsible for the observed acceleration and because the graviton is massive, the contribution of vacuum energy to the acceleration of the universe is much smaller than what general relativity predicts.

An attractive property of massive gravity is that while the graviton mass is extremely small compared to all other particles of the standard model, it remains small even when you include effect of quantum corrections, so it is technically natural. In GR the graviton is massless and of course we know that a mass will not be generated by quantum correction. This is forbidden by local symmetries. As soon as we give the graviton a mass, it of course receives quantum corrections, however in the case of massive gravity, the radiative corrections to the mass are themselves proportional to the mass. This is a little more subtle than t’Hooft naturalness argument for global symmetries (since the symmetries recovered in the massless limit are local), but it is a technical naturalness quality that we able to show. This is in contrast to the cosmological constant which is unstable under quantum corrections, the cosmological constant receives radiate corrections which are unrelated to its actual value.

**What experimental ways are there to test massive gravity? **

Perhaps one of the most cleanest ways is through observations of gravitational waves. If the graviton is massive, the gravitational waves would have a modified dispersion relation: high-frequency waves will travel faster compared to low-frequency ones. So with the LIGO observations and from the absence of such a modification of the dispersion relation one can put a limit on the graviton’s mass, which has to be smaller than 10^{-21} eV. This seems very small but we are thinking more of a cosmological mass for the graviton which has to be around 10^{-32}-10^{-33} eV; still ten orders of magnitude below what we get from LIGO.

The other set of constraints come from the fact that we can have an additional channel of radiation because you don’t have just the two polarizations but you have additional excitations. So systems of objects spinning around each other (like neutron stars) could lose energy more rapidly as they emit in more channels. We have some constraints from binary pulsars that have been observed over years and we have a good control of how much energy is lost over a certain period of time which puts another bound on the mass of the graviton though not so strong (again about 10^{-20} eV). There are also tests that offer better bounds but are more model dependent.

**Is a massive graviton compatible with a quantum theory of gravity? **

Massive gravity is a low-energy modification of gravity and doesn’t answer the question what the fundamental theory of gravity at high energy is and how gravity is quantized. One might think that massive gravity is just a theory at low energy while there should be another one at high-energy scales and these two things know little about each other. This is roughly correct at first sight but we can actually do much better than that ! Integrating out heavier degrees of freedom has consequences at what you see at lower energies and conversely if you think about it from a low-energy effective field theory perspective, the type of operators you have would lead to a particular class of UV completions. So even though we don’t know what the UV completion of massive gravity is, we impose a lot of constraints to make sure that it could enjoy a meaningful UV completion.

**There are alternative models that attempt to explain dark energy by introducing new fields. Do you think that our understanding of dark energy will involve only a modification of gravity or also of the standard model of particle physics? **

There is a fundamental question concerning what you really try to modify. If you think about modifying the gravitational degrees of freedom, the standard polarisations of the graviton, at large distances it would effectively be like giving a mass to the graviton. There are alternative ways to modify gravity by introducing by hand additional degrees of freedom. These don’t affect directly how the graviton behaves but can give you additional degrees of freedom that may or may not be linked to gravity.

In my view, If you start adding additional scalars or vectors in their own right then this is in the framework of dark energy. You have gravity and additional degrees of freedom that you add by hand and may or may not couple with gravity in a minimal way and may slightly modify the properties of gravity like the propagation of gravitational waves, but this modification is not intrinsic to gravity itself.

In that sense, a lot of alternative models introduce additional fields, scalars, vectors etc, but they don’t tackle the cosmological constant problem. They put the cosmological constant to zero and then try to explain dark energy. In many models of gravity that rely on additional fields to explain dark energy, the tuning present in the mass or coupling of these extra fields is typically as large as the cosmological constant tuning. So you haven’t solved the cosmological constant problem in the first place and you introduce a new parameter that is not natural; a new naturalness issue in that sense.

The models that try to introduce additional fields to tackle the cosmological constant problem itself but not many. We know from Weinberg’s no-go theorem that within the context of GR, any standard type of field introduced to explain dark energy or address the cosmological constant problem typically has a similar type of tuning involved.

**Do you think that it is important to communicate our scientific efforts?**

Fundamentally what we do interests and excites the public that wants to learn more about our research. As scientists we have this culture of exchange and sharing. Communicating to the public sometimes also helps to put things on a more concrete basis.

Of course there are different levels of what we share. I have pages of calculations that probably I will not share with the public. You share the work that is more polished and gives the big picture of the story.

Moreover, the news on the discovery of gravitational waves or the Higgs boson in a way may give a biased impression to the public. Of course it is important to share these discoveries that also offer the opportunity to reach a wider audience and discuss about our research, however the public often thinks that a new discovery is a complete package; a happy-ending for the scientific community.

I think we shouldn’t be afraid to crack open our research and also emphasize the number of things we don’t understand. This is actually the reason we continue to do fundamental research. When the Higgs boson was discovered many people ask: “now what?”, “why do we need to continue with particle physics?”. This was the case with the announcement of the gravitational wave detection, generating big headlines like “Einstein was right”.

But this is not at all the point of scientific research. It makes it sound as if it is the end of the story, while in reality every discovery is the beginning of a new era. We don’t do research to prove if someone was right or wrong. We do research to learn from it and move forward and this is an important point that we should include in our communication efforts. We are all explorers and the public loves taking part in this exploration.