\begin{document}$ \Omega_{\rm{gw}}h^{2} $\end{document}, by analyzing Planck, ACT, SPT CMB, and DESI BAO data combinations. In the standard cosmological model, we establish 95% CL upper limits of \begin{document}$ \Omega_{\rm{gw}}h^{2} < 1.0 \times 10^{-6} $\end{document} for adiabatic initial conditions and \begin{document}$ \Omega_{\rm{gw}}h^{2} < 2.7 \times 10^{-7} $\end{document} for homogeneous initial conditions, assuming a uniform prior for \begin{document}$ \Omega_{\rm gw}h^{2} $\end{document}. In light of dynamical dark energy, we obtain \begin{document}$ \Omega_{\rm{gw}}h^{2} < 7.2 \times 10^{-7} $\end{document} (adiabatic) and \begin{document}$ \Omega_{\rm{gw}}h^{2} < 2.4 \times 10^{-7} $\end{document} (homogeneous). In contrast, if a log-uniform prior is assumed for \begin{document}$ \Omega_{\rm gw}h^{2} $\end{document}, these constraints become tighter by a factor of approximately 4, suggesting the results are prior-sensitive. Furthermore, we project the sensitivity achievable with LiteBIRD and CMB Stage-IV measurements of CMB and CSST observations of BAO, forecasting 68% CL uncertainties of \begin{document}$ \sigma = 2.5 \times 10^{-7} $\end{document} (adiabatic) and \begin{document}$ \sigma = 1.0 \times 10^{-7} $\end{document} (homogeneous) for \begin{document}$ {\Omega_{\rm{gw}}h^{2}} $\end{document}. The constraints obtained in this work provide critical benchmarks for exploring the cosmological origins of gravitational waves within the frequency band \begin{document}$ f \gtrsim 10^{-15} $\end{document} Hz and potentially enable joint analysis with direct gravitational-wave detection sensitive to this regime."> New constraints on cosmological gravitational waves from CMB and BAO in light of dynamical dark energy -
  • [1]

    L. Bian, R. G. Cai, Y. Q. Donget al.,Sci. China Phys. Mech. Astron.69, 210401 (2026)

  • [2]

    C. P. Ma and E. Bertschinger, Astrophys. J.455, 7 (1995), arXiv: astro-ph/9506072

  • [3]

    M. Bucher, K. Moodley, and N. Turok, Phys. Rev. D62, 083508 (2000), arXiv: astro-ph/9904231

  • [4]

    R. Abbottet al. (KAGRA and Virgo and LIGO Scientific collaboration), Phys. Rev. D104, 022004 (2021), arXiv: 2101.12130

  • [5]

    H. Xu, S. Chen, Y. Guoet al., Res. Astron. Astrophys.23, 075024 (2023), arXiv: 2306.16216

  • [6]

    J. Antoniadiset al. (EPTA and InPTA: collaborations), Astron. Astrophys.678, A50 (2023), arXiv: 2306.16214

  • [7]

    G. Agazieet al. (NANOGrav collaboration),Astrophys. J. Lett.951, L8 (2023), arXiv: 2306.16213

  • [8]

    D. J. Reardon, A. Zic, R. M. Shannonet al.,Astrophys. J. Lett.951, L6 (2023), arXiv: 2306.16215

  • [9]

    W. R. Hu and Y. L. Wu, Natl. Sci. Rev.4, 685 (2017)

  • [10]

    M. Colpiet al., arXiv: 2402.07571

  • [11]

    J. Luoet al. (TianQin collaboration), Class. Quant. Grav.33, 035010 (2016), arXiv: 1512.02076

  • [12]

    T. L. Smith, E. Pierpaoli, and M. Kamionkowski, Phys. Rev. Lett.97, 021301 (2006), arXiv: astro-ph/0603144

  • [13]

    T. J. Clarke, E. J. Copeland, and A. Moss,JCAP10, 002 (2020), arXiv: 2004.11396

  • [14]

    G. Cabass, L. Pagano, L. Salvatiet al., Phys. Rev. D93, 063508 (2016), arXiv: 1511.05146

  • [15]

    X. J. Liu, W. Zhao, Y. Zhanget al., Phys. Rev. D93, 024031 (2016), arXiv: 1509.03524

  • [16]

    S. Vagnozzi, JHEAp39, 81 (2023), arXiv: 2306.16912

  • [17]

    T. Bringmann, P. F. Depta, T. Konstandinet al., JCAP11, 053 (2023), arXiv: 2306.09411

  • [18]

    S. Wang, Z. C. Zhao, and Q. H. Zhu, Phys. Rev. Res.6, 013207 (2024), arXiv: 2307.03095

  • [19]

    Q. H. Zhu, Z. C. Zhao, S. Wanget al., Chin. Phys. C48, 125105 (2024), arXiv: 2307.13574

  • [20]

    J. Z. Zhou, Y. T. Kuang, Z. Changet al., Astrophys. J.979, 178 (2025), arXiv: 2410.10111

  • [21]

    J. Z. Zhou, Z. C. Li, and D. Wu,Phys. Rev. D112, 063511 (2025), arXiv: 2505.22614

  • [22]

    D. Wu, J. Z. Zhou, Y. T. Kuanget al., JCAP03, 045 (2025), arXiv: 2501.00228

  • [23]

    M. Abdul Karimet al. (DESI collaboration),Phys. Rev. D112, 083515 (2025), arXiv: 2503.14738

  • [24]

    H. Wang, Z. Y. Peng, and Y. S. Piao, arXiv: 2503.2391

  • [25]

    E. Allyset al. (LiteBIRD Collaboration), PTEP2023, 042F01 (2023), arXiv: 2202.02773

  • [26]

    K. N. Abazajianet al. (CMB-S4 Collaboration), arXiv: 1610.02743

  • [27]

    Y. Gong, X. Liu, Y. Caoet al., Astrophys. J.883, 203 (2019), arXiv: 1901.04634

  • [28]

    D. Blas, J. Lesgourgues, and T. Tram, JCAP07, 034 (2011), arXiv: 1104.2933

  • [29]

    N. Aghanimet al. (Planck Collaboration), Astron. Astrophys.641, A6 (2020), arXiv: 1807.06209

  • [30]

    M. Chevallier and D. Polarski, Int. J. Mod. Phys. D10, 213 (2001), arXiv: gr-qc/0009008

  • [31]

    E. V. Linder, Phys. Rev. Lett.90, 091301 (2003), arXiv: astro-ph/0208512

  • [32]

    E. Camphuiset al. (SPT-3G collaboration), arXiv: 2506.20707

  • [33]

    J. Carron, M. Mirmelstein, and A. Lewis, JCAP09, 039 (2022), arXiv: 2206.07773

  • [34]

    SPT-3G collaboration, Phys. Rev. D111, 083534 (2025), arXiv: 2411.06000

  • [35]

    F. J. Quet al. (SPT-3G and ACT Collaborations), arXiv: 2504.20038

  • [36]

    T. Louiset al. (ACT Collaboration), arXiv: 2503.14452

  • [37]

    J. Torrado and A. Lewis, JCAP05, 057 (2021), arXiv: 2005.05290

  • [38]

    T. Brinckmann and J. Lesgourgues, Phys. Dark Univ.24, 100260 (2019), arXiv: 1804.07261

  • [39]

    B. Audren, J. Lesgourgues, K. Benabedet al., JCAP02, 001 (2013), arXiv: 1210.7183

  • [40]

    H. Miao, Y. Gong, X. Chenet al., Mon. Not. Roy. Astron. Soc.531, 3991 (2024), arXiv: 2311.16903

  • [41]

    R. Kou and A. Lewis, JCAP08, 031 (2025), arXiv: 2504.13913

  • [42]

    A. Afzalet al. (NANOGrav Collaboration), Astrophys. J. Lett.951, L11 (2023), arXiv: 2306.16219

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