11322 2203.00619 10.1140/epjc/s10052-023-11322-3 193 9 Perturbations in non-flat cosmology for f(T) gravity Regular Article - Theoretical Physics 1 17 2023 2 14 2023 1 6 2023 2 11 2023 3 6 Nazarbayev University 11022021FD2926 Eesti Teadusagentuur PRG356 Hellenic Foundation for Research and Innovation 2251 European Regional Development Fund TK133 Japan Society for the Promotion of Science JP21F21789 Deutsche Forschungsgemeinschaft 420243324 The Author(s) 2023 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development. 10052 83 83 3 3 Sebastian Bahamonde sbahamondebeltran@gmail.com bahamonde.s.aa@m.titech.ac.jp Konstantinos F. Dialektopoulos kdialekt@gmail.com Manuel Hohmann manuel.hohmann@ut.ee Jackson Levi Said jackson.said@um.edu.mt Christian Pfeifer christian.pfeifer@zarm.uni-bremen.de Emmanuel N. Saridakis msaridak@noa.gr grid.32197.3e 0000 0001 2179 2105 Department of Physics Tokyo Institute of Technology 1-12-1 Ookayama, Meguro-ku Tokyo 152-8551 Japan grid.10939.32 0000 0001 0943 7661 Laboratory of Theoretical Physics, Institute of Physics University of Tartu W. Ostwaldi 1 50411 Tartu Estonia grid.4793.9 0000000109457005 Laboratory of Physics, Faculty of Engineering Aristotle University of Thessaloniki Thessaloniki 54124 Greece grid.428191.7 0000 0004 0495 7803 Department of Physics Nazarbayev University 53 Kabanbay Batyr avenue 010000 Astana Kazakhstan grid.4462.4 0000 0001 2176 9482 Institute of Space Sciences and Astronomy University of Malta Msida Malta grid.4462.4 0000 0001 2176 9482 Department of Physics University of Malta Msida Malta grid.7704.4 0000 0001 2297 4381 ZARM University of Bremen 28359 Bremen Germany grid.8663.b 0000 0004 0635 693X National Observatory of Athens Lofos Nymfon 11852 Athens Greece grid.59053.3a 0000000121679639 CAS Key Laboratory for Research in Galaxies and Cosmology University of Science and Technology of China Hefei 230026 Anhui China Abstract The study of cosmological perturbation theory in f(T) gravity is a topic of great interest in teleparallel gravity since this is one of the simplest generalizations of the theory that modifies the teleparallel equivalent of general relativity. In this work, we explore the possibility of a non-flat FLRW background solution and perform perturbations for positively as well as negatively curved spatial geometries, together with a comparison to the flat case. We determine the generalized behaviour of the perturbative modes for this non-flat FLRW setting for arbitrary f(T) models, when the most general homogeneous and isotropic background tetrads are used. We also identify propagating modes in this setup, and relate this with the case of a flat cosmology.