Physics of the Dark Universe 35 (2022) 100956 Contents lists available at ScienceDirect Physics of the Dark Universe journal homepage: www.elsevier.com/locate/dark Modified Teleparallel Gravity induced by quantum fluctuations Che-Yu Chen a , Yu-Hsien Kung b,c ,∗ a Institute of Physics, Academia Sinica, Taipei 11529, Taiwan b Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan c Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan article info Article history: Received 27 November 2021 Received in revised form 11 January 2022 Accepted 14 January 2022 abstract In the semi-classical regime, quantum fluctuations embedded in a Riemannian spacetime can be effectively recast as classical back reactions and manifest themselves in the form of non-minimal couplings between matter and curvature. In this work, we exhibit that this semi-classical description can also be applied within the teleparallel formulation. In the teleparallel formulation, quantum fluctuations generically lead to non-minimal torsion–matter couplings. Due to the equivalence between the (classical) Einstein gravity in the Riemannian description and that in teleparallel description, some effective models which were constructed using Riemannian description can be reproduced completely using the teleparallel description. Besides, when the effective quantum correction term is proportional to the torsion scalar T , we obtain a subclass of novel f (T , B, T ) gravity, where B is a boundary term, and T is the trace of the energy–momentum tensor. Next, we investigate the cosmological properties in this f (T , B, T ) theory by assuming that the matter Lagrangian is solely constructed by a dynamical scalar field. We exhibit some interesting cosmological solutions, such as those with decelerating expansion followed by a late-time accelerating phase. In addition, the non-minimal torsion–matter couplings induced by quantum corrections naturally lead to energy transfers between gravity and cosmological fluids in the universe. © 2022 Elsevier B.V. All rights reserved. 1. Introduction Although Einstein’s General Relativity (GR) is very successful in describing our universe, it still suffers from several essential puzzles. From the theoretical point of view, it is still not clear how to consistently embed quantum effects into the framework of GR. In fact, the consistent formulation of a fundamental quantum theory of gravity is still lacking. From the observational perspec- tives, on the other hand, the observations of recent accelerating expansion of the universe, as well as the mysterious existence of some ‘‘unseeable’’ matter fields clustering around galaxies and galaxy clusters, challenge our current understanding of cosmol- ogy. The simplest explanation of these exotic phenomena may be the inclusion of some non-standard matter fields, such as dark energy and dark matter, respectively. However, some problems still remain. For example, the questions that where these dark sectors come from, why the amount of dark energy is so tiny, and why the relative amount of dark energy and dark matter is so fine-tuned, are still open issues. ∗ Corresponding author at: Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan. E-mail addresses: b97202056@gmail.com (C.-Y. Chen), r06222010@g.ntu.edu.tw (Y.-H. Kung). In order to address the aforementioned theoretical and ob- servational issues, one phenomenological approach is to consider modified theories of GR [1]. In particular, these modified theories of gravity are expected to not only retain the success that has been achieved by GR, but also shed some light on ameliorating the fundamental puzzles mentioned above. One important ingredient within this framework is how to motivate the idea of modified theories of gravity from quantum origins. Such a connection can indeed be realized, at least, within the semi-classical regimes. In fact, in quantum mechanical descriptions of gravity, one can naively replace all the classical quantities in GR by some quantum operators. In this regard, the classical Einstein equation can then be replaced by an operator equation: ˆ G μν = 8π G c 4 ˆ T μν , (1.1) where G μν and T μν are the Einstein tensor and the energy– momentum tensor, respectively. G and c are the gravitational constant and the speed of light. The hat denotes the operator of the field. This operator equation is in general very difficult to solve, but it could be dealt with in the semi-classical regimes based on some assumptions about the expectation values of metric operators. In Refs. [2,3], the authors proposed an idea to solve Eq. (1.1) within the semi-classical approximations. It was assumed that, https://doi.org/10.1016/j.dark.2022.100956 2212-6864/© 2022 Elsevier B.V. All rights reserved.