# A7 - Cosmology with Graviton Condensates

#### Principal Investigator: G. Dvali (Munich), St. Hofmann (Garching)

## Summary

The project's main objective is to apply to cosmological and other gravitational backgrounds a recently suggested approach (by Dvali and Gomez) of viewing the space-time geometry as a quantum state of gravitons with large occupation number N. That is, in this approach the geometry is viewed as some sort of a Bose-Einstein condensate (BEC) of gravitons. The conventional description in terms of the classical metric is fully emergent in this picture, as a result of the N → ∞ limit. This emergence is analogous to the description of a classical electromagnetic wave in terms of a large photon occupation number.
The advantage of this approach is that it is intrinsically-quantum and treats different space-times as different quantum states of graviton BEC on the Minkowski vacuum. In most of the cases we are dealing with low curvature backgrounds, which in the BEC language translate as states with long-avelength gravitons, much longer than the Planck length, LP ~ 10-33cm. Thus, our approach is insensitive to the particular nature of ultra-violet completion of gravity beyond the Planck length, and interactions of gravitons can be reliably treated in the framework of low energy effective theory with vertices given by the usual expansion of Einstein’s action in terms of weakly coupled gravitons.
Thus, while having a fully legitimate approach to quantum gravity, we are not entering the domain of UV-completion (trans-Planckian energies). This fact is important to be stressed, since these two notions are sometimes confused in the scientific community, due to an implicit assumption that the quantum interactions of gravitons only become important at Planck distances and are irrelevant at long wave-lengths. As was uncovered by Dvali and Gomez, this assumption in general breaks down when the occupation number N of gravitons is large and certain criticality conditions are fulfilled. In such a case, quantum gravity corrections become vital even for macroscopic systems (such as macroscopic black holes and cosmological backgrounds).
The novelty of our approach is obvious. It allows us to treat geometry as an emergent quantummechanical entity and capture effects that are unaccessible in the standard semi-classical treatment. These effects turn out to be extremely important in certain cases, when the background is at the point of a so-called quantum phase transition. At this point even macroscopic system becomes fully sensitive to quantum dynamics and cannot be understood classically.
This opens up an entirely new avenue for viewing the dynamics of space-time geometry and grants the possibility to approach questions that simply cannot be addressed in the standard framework. Such are, for example, the questions of information loss by black holes and cosmological singularities. Unlike black holes, cosmological backgrounds require an external source in form of a cosmic fluid and a vacuum energy density. In many respects, nevertheless, cosmological horizons share similarities with black holes. For instance, the Universe inside a Hubble sphere can be thought of entering a gravitational collapse towards black hole formation, but the cosmic expansion counteracts it. As a consequence, an observer never crosses the horizon of such a would-be "black hole". This analogy encourages us to generalize the BEC perspective on black holes to cosmological backgrounds, and to describe the geometry of our Universe accordingly.
We are convinced that this approach can shed some very different light on the consistency of cosmological backgrounds that can never be seen in the conventional classical treatment of the geometry. For example, we can prove explicitly that certain inflationary or Dark Energy scenarios violate new consistency bounds originating within the quantum framework described above.
Non-perturbative aspects of graviton condensation lead to a rich vacuum structure that can be parametrized using a few condensates only. All weakly coupled degrees of freedom respond by adjusting their dynamics according to the induced in-medium modification. This allows to describe geometrical effects entirely within the standard field theoretical framework. We will predict momentum distributions of gravitons within cosmological geometries and describe global characteristics such as our Universe’s vacuum energy density as bound state properties. This might offer a 't Hooft natural explanation for the smallness of the cosmological constant. Complementary to this approach we plan to develop a graviton flux representation of geometry. Again, these flux tubes can be expanded in terms of graviton condensates. This amounts to the full "de-geomtrization" of space-time physics and cosmology, in particular. Standing challenges can be addressed in this framework and new questions can be asked simply because the framework developed here is applicable even beyond semi-classicality. As a good example for this serves the cosmological singularity challenge, which we expect to turn out to be a geometrical misconception with no bearing on the more fundamental bound state description. Consequences for inflation will be explored.

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