We show that the Nieh-Yan topological invariant breaks projective symmetry and loses its topological character in presence of non vanishing nonmetricity. The notion of the Nieh-Yan topological invariant is then extended to the generic metric-affine case, defining a generalized Nieh-Yan term, which allows to recover topologicity and projective invariance, independently. As a concrete example a class of modified theories of gravity is considered and its dynamical properties are investigated in a cosmological setting. In particular, bouncing cosmological solutions in Bianchi I models are derived. Finite time singularities affecting these solutions are analysed, showing that the geodesic completeness and the regular behavior of scalar perturbations in these space-times are not spoiled.
Chiral Gravitational Wave Background from Audible Axion via Nieh-Yan Term
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学学院）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文学与空间科学学院）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）；International Center for Theoretical Physics Asia-Pacific (ICTP-AP), University of Chinese Academy of Sciences（中国科学院大学国际理论物理中心亚太地区）；Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences（中国科学院大学太极引力波宇宙实验室（北京/杭州））；CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所理论物理重点实验室）
Realization of quintom dark energy after DESI DR2 in Nieh-Yan modified teleparallel gravity
University of Science and Technology of China（中国科学技术大学）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学交叉理论研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）
Inflation with Nieh-Yan-like terms in metric-affine gravity
University of Tartu（塔尔图大学）；National Institute of Chemical Physics and Biophysics（生物物理与化学物理国家研究所）；Scuola Superiore Meridionale（南方高等学院）；INFN– Sezione di Napoli（意大利国家核物理研究院那不勒斯分部）
Twisting inflation to sub-Planckian axion decay constants
Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学）；Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh（爱丁堡大学）；Physics and Applied Mathematics Unit, Indian Statistical Institute（印度统计研究所）
