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Teleparallel Palatini theories
Univ Autonoma Madrid, CSIC, Inst Fis Teor, E-28049 Madrid, Spain.;Univ Salamanca, Dept Fis Fundamental, Plaza Merced, E-37008 Salamanca, Spain..
Swiss Fed Inst Technol, Inst Theoret Studies, Clausiusstr 47, CH-8092 Zurich, Switzerland..
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.ORCID iD: 0000-0002-9403-8565
2018 (English)In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 8, article id 039Article in journal (Refereed) Published
Abstract [en]

The Palatini formalism, which assumes the metric and the affine connection as independent variables, is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, as done in the usual teleparallel theories, but we follow a completely covariant approach by imposing the constraints with suitable Lagrange multipliers. For a general quadratic theory we show how torsion naturally propagates and we reproduce the Teleparallel Equivalent of General Relativity as a particular quadratic action that features an additional Lorentz symmetry. We then study the much less explored theories formulated in a geometry with neither curvature nor torsion, so that all the geometrical information is encoded in the non-metricity. We discuss how this geometrical framework leads to a purely inertial connection that can thus be completely removed by a coordinate gauge choice, the coincident gauge. From the quadratic theory we recover a simpler formulation of General Relativity in the form of the Einstein action, which enjoys an enhanced symmetry that reduces to a second linearised diffeomorphism at linear order. More general theories in both geometries can be formulated consistently by taking into account the inertial connection and the associated additional degrees of freedom. As immediate applications, the new cosmological equations and their Newtonian limit are considered, where the role of the lapse in the consistency of the equations is clarified, and the Schwarzschild black hole entropy is computed by evaluating the corresponding Euclidean action. We discuss how the boundary terms in the usual formulation of General Relativity are related to different choices of coordinates in its coincident version and show that in isotropic coordinates the Euclidean action is finite without the need to introduce boundary or normalisation terms. Finally, we discuss the double-copy structure of the gravity amplitudes and the bootstrapping of gravity within the framework of coincident General Relativity.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018. no 8, article id 039
Keywords [en]
gravity, modified gravity
National Category
Geometry
Identifiers
URN: urn:nbn:se:kth:diva-234614DOI: 10.1088/1475-7516/2018/08/039ISI: 000443020600001Scopus ID: 2-s2.0-85053117948OAI: oai:DiVA.org:kth-234614DiVA, id: diva2:1248163
Note

QC 20180914

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2018-10-16Bibliographically approved

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Koivisto, Tomi S.

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