20thcentury physics totally changed the way we understood the world by giving birth to two revolutionary theories, General Relativity and Quantum Mechanics. However, it has left us with a giant puzzle which might turn to be the seed of a new revolution: Instead of having a single theoretical framework with which to understand nature, we have two, and two which are mutually inconsistent, at least as far as we can see. In order to describe a system or process in physics we have first to decide which of these two realm it belongs to. Then, we can proceed with the corresponding machinery. The situation is not particularly appealing, but one might pass over in silence if there were no system or process belonging to both realms at once. But this is not the case, there are at least two situations that ask for General Relativity and Quantum Mechanics at the same time: The formation and evolution of black holes and the origin and evolution of the Universe as a whole, the subject of Cosmology. Without a combined theory of gravity and the quantum we will be unable to understand such fundamental systems.
The main activity of our group is to investigate these two situations and to search for ways of combining the gravitational and the quantum realms. For that we use a wide range of techniques: From numerical simulations in full General Relativity to grouptheoretical and condensed matter techniques.
This research line of the IAA contains a number of specific subtopics that we pass now to briefly describe.

Grouptheoretical quantization: We are further developing the grouptheoretical quantization scheme to attack the problem of quantization of General Relativity or at least, of subsectors of it reduced by symmetry considerations. To apply these techniques we are firstly developing a gauge theoretical version of General Relativity mixed other interactions such that the internal and spacetime symmetries appear on an equal footing.

Numerical simulations of black holes mergers: We are interested in the dynamics of gravitational systems possessing horizons from a double perspective. From the observational/astrophysical side, we are working in calculating the gravitational wave emission characterizing the dynamics of these system and preparing for the extraction of physical parameters from the future interferometric observations. From the theoretical side, we are developing the characterization of these systems in terms of the local notion of dynamical and trapping horizons.

Gravitational collapse in theories of gravity beyond Einstein's Generel Relativity: We are interested in making a comparison between the collapse process in standard General Relativity and that in other gravitational theories that incorporate modifications to General Relativity. In particular we are analyzing the collapse process in the simplest quantum corrected version of General Relativity, the socalled semiclassical General Relativity. We have already seen that for certain initial classical models of collapse the semiclassical corrections could be important even before the formation of the horizon.

Analogue Gravity: Condensed matter systems with emergent geometrical properties have already proved very important in understanding which type of quantum corrections one could expect to see when probing gravity at high energies. By analyzing the behaviour of artificial black holes and expanding universes build within condensed matter systems (for example, BoseEinstein Condensates) we plan to continue obtaining insights about plausible departures from standard General Relativity.

Dark energy from microscopic degrees of freedom: We are interested on understanding the origin of the dark energy in the universe starting from first principles. The analogies with liquidlike systems in condensed matter offer a very interesting framework in which to investigate this issue. This has already motivate us to propose a new cosmological model in which dark energy and dark matter are not conserved independently.

The origin of the mass of the particles: One of the biggest problems in physics is to understand what it is the origin of the mass of elementary particles. In the standard model of particle physics the mass emerge owing to the interaction of the Higgs particle with initially massless fermions. In our group we are investigating an alternative mechanism that does not need the existence of the Higgs. It relies on the possibility of mixing gravity with other interactions and on the grouptheoretical quantization of nonAbelian YangMills theories. These analysis are in perfect timing with the scheduled probe of the existence of the Higgs in the LHC at CERN.
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