Selected Papers from Teleparallel Universes in Salamanca

Dear Colleagues,

Gravity is commonly understood as a geometric phenomenon. This understanding goes back to Einstein's formulation of the General Theory of Relativity, which attributes gravity to the curvature of spacetime. The great insight underlying this theory was the unification of gravity and inertia, which allows the geometric description of the gravitational interaction as spacetime curvature anticipated by both Riemann and Clifford.

However, equivalent descriptions are known in terms of torsion and non-metricity. Due to the flatness of the connection in these alternative formulations, they are called teleparallel theories. It is timely to explore gravity in this alternative framework, as the conventional version of General Relativity, despite its great success in describing numerous phenomena, is being challenged by many observational and conceptual problems. The most prominent observational issues are cosmological: the Universe, as described by General Relativity, seems to be filled with invisible matter and unexplained energy whose density remains nearly constant in the expanding space. The conceptual issues are mostly related to quantum theory: notoriously, gravity has not been quantised, and foundational questions regarding the nature of space and time remain without conclusive answers.

The analysis of General Relativity in generalised geometry was begun by Hermann Weyl a century ago in 1918, and it eventually lead to the development of the gauge theories comprising the modern standard model of particle physics. Nevertheless, the theory of gravity remains to be unified in this context. Like the other fundamental interactions of nature, we believe that gravitation also can be described in terms of a gauge theory, and, in particular, teleparallel formulations have been considered as gauge theories of the group of translations. Elie Cartan had laid important mathematical foundations by introducing the concepts of moving frames and torsion. One of the well-known frameworks wherein teleparallelism may be naturally embedded is metric affine gauge theory, featuring both Weyl’s non-metricity and Cartan’s torsion.

This Special Issue of Universe reports proceedings of the workshop Teleparallel Universes in Salamanca (26-28 November 2018). The research and review articles will reflect recent developments at the frontiers of teleparallel theory. Different covariant formulations are presented, and the theory is approached from the premetric perspective and in terms of Cartan geometry. The important and open issue of the degrees of freedom in generalised theories is discussed in several papers using the Hamiltonian formalism. The phenomenology of teleparallel theories is considered in the framework of black holes and cosmology. A reappraisal of cosmology based on teleparallel gravity could provide a new way to look at the Universe, unveiling perspectives that may resolve the cosmological constant problem, the nature of dark energy and dark matter, and the genesis of the Universe in the inflationary or alternative scenarios.

Prof. Dr. Tomi Koivisto
Dr. Jose Beltran Jimenez
Dr. Lavinia Heisenberg
Dr. Alexey Golovnev
Guest Editors

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