# Can gravity be massless

## Without “ghosts”: A new theory of gravity

### Research Report 2018 - Max Planck Institute for Physics

In many ways, gravity is a very special physical phenomenon. It is the only force of nature that we can actually perceive as gravity. At the same time, however, it is also by far the weakest of all known natural forces. For theoretical physicists it represents a great and exciting challenge. Because over 100 years after Albert Einstein's development of the general theory of relativity, the theoretical description of gravity still raises many questions. The long-term goal of my group's work is to reconcile this exotic force with other established physical models.

### Properties of the particle of gravity

The standard model of particle physics is one of these proven theories. It provides a mathematical, field-theoretical description of all elementary particles and the forces that act on them. In a field theory, each point in space is assigned one or more field values that characterize the physical state. Each field ultimately corresponds to a type of particle.

In recent years it has been possible to check the standard model with high precision. A characteristic property of the particles is an internal angular momentum quantum number, called spin. For example, the Higgs boson, which is responsible for the mass of the particles, has a spin number of 0, the electron has a spin number of 1/2, and the photon (the mediator of electromagnetic force) has a spin of 1. Some of these particles have one Mass, others are massless. Regardless of the mass, field theories for particles with a spin number smaller than 2 are very well understood.

The general theory of relativity, on the other hand, postulates a hypothetical particle with a spin number of 2 that mediates the force of gravity: the graviton. This is massless by definition, and its description by the general theory of relativity has meanwhile been very thoroughly investigated. For many decades theorists tried in vain to describe a massive spin-2 particle. Why?

Particles with a spin number less than 2 can be massless as well as massive and occur in nature in both forms. Therefore it seems logical that a massive spin-2 particle should also be theoretically describable and possibly exist. The description of such an elementary particle is an important missing piece of the puzzle in the totality of all mathematically consistent field theories.

### Description of a massive spin-2 particle

In 2011 the problem of the field theoretical description of massive spin-2 particles was finally solved. The corresponding theory is an extension of the general relativity theory with a very special mathematical structure. We call it Ghost-Free Bimetric Theory (short: Bimetric Theory). Because their special structure avoids a mathematical inconsistency, a so-called ghost, which was a problem in earlier proposed theories. The bimetric theory describes both a massive and a massless spin-2 particle that interact with each other.

Although the gap in the missing theory of the massive spin-2 particle has now been closed, there are still many more questions to be answered. One of the most important is that based on a quantum theory of gravity. The standard model for particles with a spin number less than 2 is such a quantum field theory, a combination of field and quantum theory. On the other hand, general relativity is a classical field theory that we do not know for sure how to reconcile with quantum mechanics.

String theory offers a promising proposal for a unification of gravitation and quantum physics. This does not describe particles as point-like objects, but with the help of one-dimensional strings. String theory is a very elegant possible solution to the problem of quantum gravity. But we don't know exactly how it relates to the Standard Model and its verifiable predictions.

### Conformal Gravity without "ghost"

The research field of my working group is bimetric theory and its classification in the overall concept of theoretical physics. We are particularly interested in a possible connection with string theory. In the past year we have taken an important step closer to this goal [1, 2]. We succeeded in proving an exact relation between the bimetric theory and another theory called conformal gravity. Conformal gravity is also a theory of gravity that has received a lot of attention in the past. However, unlike the Bimetric Theory, it suffers from inconsistencies caused by a spirit similar to the one mentioned above.

Our work shows how one can free conformal gravity from their spirit. To do this, one has to add missing contributions to the field theoretical description. The resulting, completed theory then corresponds exactly to our bimetric theory. Since the relationship between conformal gravity and string theory is already better understood, we now hope that we can finally deduce from this how bimetric theory and string theory are related. In order to achieve this, however, we are still missing a few important intermediate steps.

For example, we need a supersymmetrized version of our bimetric theory. Supersymmetry is a necessary part of string theory. Its realization is very well understood in field theories for particles with a spin number smaller than 2. The supersymmetrized version of general relativity is also known. The group is currently looking for the supersymmetric theory for massive spin-2 particles, which will hopefully bring us one step closer to string theory.

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