13998 2409.17846 10.1140/epjc/s10052-025-13998-1 327 107 Constraining string cosmology with the gravitational-wave background using the NANOGrav 15-year data set 01 Mathematical Sciences 0104 Statistics Regular Article - Theoretical Physics Theoretical Physics 1 9 2025 2 25 2024 12 26 2025 2 21 2025 3 21 National Natural Science Foundation of China 12347111 12405055 12405057 12433001 China Postdoctoral Science Foundation 2023M741148 The Author(s) 2025 Open Access This 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. 10052 85 85 3 3 Qin Tan tanqin@hunnu.edu.cn You Wu youwuphy@gmail.com Lang Liu liulang@bnu.edu.cn https://ror.org/053w1zy07 grid.411427.5 0000 0001 0089 3695 Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications Hunan Normal University Changsha 410081 Hunan China https://ror.org/053w1zy07 grid.411427.5 0000 0001 0089 3695 Institute of Interdisciplinary Studies Hunan Normal University Changsha Hunan 410081 China https://ror.org/01ggnn306 grid.440778.8 0000 0004 1759 9670 College of Mathematics and Physics Hunan University of Arts and Science Changde 415000 China https://ror.org/022k4wk35 grid.20513.35 0000 0004 1789 9964 Faculty of Arts and Sciences Beijing Normal University Zhuhai 519087 China Abstract Multiple pulsar timing array (PTA) collaborations, including the European PTA in partnership with the Indian PTA, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the Parkes PTA, and the Chinese PTA have recently reported strong evidence for a signal at nanohertz, potentially the first detection of the stochastic gravitational-wave background (SGWB). We investigate whether the NANOGrav signal is consistent with the SGWB predicted by string cosmology models. By performing Bayesian parameter estimation on the NANOGrav 15-year data set, we constrain the key parameters of a string cosmology model: the frequency f s and the fractional energy density Ω gw s of gravitational waves at the end of the dilaton-driven stage, and the Hubble parameter H r at the end of the string phase. Our analysis yields constraints of f s = 1 . 2 - 0.6 + 0.6 × 10 - 8 Hz and Ω gw s = 2 . 9 - 2.3 + 5.4 × 10 - 8 , consistent with theoretical predictions from string cosmology. However, the current NANOGrav data is not sensitive to the H r parameter. We also compare the string cosmology model to a simple power-law model using Bayesian model selection, finding a Bayes factor of 2.2 in favor of the string cosmology model. Future pulsar timing array observations with improved sensitivity and extended frequency coverage will enable tighter constraints on string cosmology parameters.