General teleparallel quadratic gravity
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Jiménez, J. B., Heisenberg, L., Iosifidis, D., Jiménez-Cano, A., & Koivisto, T. S. (2020). General teleparallel quadratic gravity. Physics Letters B, 135422. [DOI: 10.1016/j.physletb.2020.135422]
SponsorshipAtraccion del Talento Cientifico en Salamancaprogramme; MINECO FIS2014-52837-P FIS2016-78859-P; European Research Council (ERC) 801781; Swiss National Science Foundation (SNSF) 179740; Estonian Research Council PRF project PRG356; European Union (EU) CoE TK133; CANTATA COST (European Cooperation in Science and Technology) action, EU Framework Programme Horizon 2020 CA15117; Spanish Ministry of Economy and Competitiveness FPU15/02864
In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying both torsion and non-metricity. We provide a detailed discussion on the teleparallel equivalents of General Relativity and how the two known equivalents, formulated on Weitzenböck and symmetric teleparallel geometries respectively, can be interpreted as two gauge-fixed versions of the general teleparallel equivalent. We then explore the viability of the general quadratic theory by studying the spectrum around Minkowski. The linear theory generally contains two symmetric rank-2 fields plus a 2-form and, consequently, extra gauge symmetries are required to obtain potentially viable theories.