\begin{document}$H_0$\end{document}, a key parameter quantifying the present expansion rate of the universe, remains a subject of significant debate due to the persistent tension between early- and late-universe measurements. Strong gravitational lensing (SGL) time delays provide an independent avenue to constrain \begin{document}$H_0$\end{document}. In this paper, we utilize seven SGL systems from the TDCOSMO sample to constrain \begin{document}$H_0$\end{document}, employing the model-independent approaches: deep neural networks (DNN), Gaussian process (GP), polynomial fitting (polyfit) and Padé approximant (PA). Using these methods, we reconstruct unanchored luminosity distances from the Pantheon+ SNe Ia dataset and obtain \begin{document}$H_0=72.3^{+3.8}_{-3.6}$\end{document} km s−1 Mpc−1, \begin{document}$H_0=72.4^{+1.6}_{-1.7}$\end{document} km s−1 Mpc−1, \begin{document}$H_0=70.7^{+3.0}_{-3.1}$\end{document} km s−1 Mpc−1 and \begin{document}$H_0=74.0^{+2.7}_{-2.7}$\end{document} km s−1 Mpc−1, respectively. These estimates are consistent within 1σ level and align with local distance ladder results. Notably, the GP method achieves uncertainties that are half those of the DNN approach, whereas the DNN method offers more reliable confidence intervals in reconstruction at high redshifts. Our findings underscore the potential of these methodologies to refine constraints on \begin{document}$H_0$\end{document} and contribute to resolving the Hubble tension with future advancements."> Model-independent constraints on the Hubble constant using lensed quasars and the latest supernova -
  • [1]

    D. Hutsemekers, R. Cabanac, H. Lamyet al., Astron. Astrophys.441, 915 (2005)

  • [2]

    J. A. King, J. K. Webb, M. T. Murphyet al., Mon. Not. Roy. Astron. Soc.422, 3370 (2012)

  • [3]

    A. Mariano and L. Perivolaropoulos, Phys. Rev. D86, 083517 (2012)

  • [4]

    C. H. Lineweaver, L. Tenorio, G. F. Smootet al., Astrophys. J.470, 38 (1996)

  • [5]

    M. Tegmark, A. de Oliveira-Costa, and A. Hamilton, Phys. Rev. D68, 123523 (2003)

  • [6]

    M. Frommert and T. A. Enßlin, PoS Cosmology2009, 015 (2009)

  • [7]

    A. G. Riesset al., Astrophys. J.855(2), 136 (2018)

  • [8]

    A. G. Riesset al., Astrophys. J. Lett.934(1), L7 (2022)

  • [9]

    N. Aghanimet al. (Planck Collaboration), Astron. Astrophys.641, A6 (2020) [Erratum: Astron. Astrophys.652, C4 (2021)]

  • [10]

    E. Aubourget al., Phys. Rev. D92(12), 123516 (2015)

  • [11]

    A. Cuceu, J. Farr, P. Lemoset al., Present and Future, JCAP2019(10), 044 (2019)

  • [12]

    O. H. E. Philcox, M. M. Ivanov, M. Simonovićet al., JCAP2020(05), 032 (2020)

  • [13]

    A. G. Riess, S. Casertano, W. Yuanet al., Astrophys. J.876(1), 85 (2019)

  • [14]

    T. M. C. Abbottet al., Phys. Rev. D98(4), 043526 (2018)

  • [15]

    B. P. Abbottet al., Nature551(7678), 85 (2017)

  • [16]

    A. Kozmanyan, H. Bourdin, P. Mazzottaet al., Astron. Astrophys.621, A34 (2019)

  • [17]

    A. Domínguez, R. Wojtak, J. Finkeet al.,A new measurement of the Hubble constant and matter content of the Universe using extragalactic background light γ-ray attenuation

  • [18]

    M. Soares-Santoset al., Astrophys. J. Lett.876(1), L7 (2019)

  • [19]

    S. H. Suyuet al., Mon. Not. Roy. Astron. Soc.468(3), 2590 (2017)

  • [20]

    S. Birreret al., Mon. Not. Roy. Astron. Soc.484, 4726 (2019)

  • [21]

    K. C. Wonget al., Mon. Not. Roy. Astron. Soc.498(1), 1420 (2020)

  • [22]

    S. H. Suyu, P. J. Marshall, M. W. Augeret al., Astrophys. J.711, 201 (2010)

  • [23]

    S. H. Suyuet al., Astrophys. J. Lett.788, L35 (2014)

  • [24]

    K. C. Wonget al., Mon. Not. Roy. Astron. Soc.465(4), 4895 (2017)

  • [25]

    I. Jee, S. Suyu, E. Komatsu, C. D. Fassnachtet al.,A measurement of the Hubble constant from angular diameter distances to two gravitational lenses

  • [26]

    G. C. F. Chenet al., Mon. Not. Roy. Astron. Soc.490(2), 1743 (2019)

  • [27]

    C. E. Rusuet al., Mon. Not. Roy. Astron. Soc.498(1), 1440 (2020)

  • [28]

    A. Agnelloet al., Mon. Not. Roy. Astron. Soc.472(4), 4038 (2017)

  • [29]

    A. J. Shajibet al., Mon. Not. Roy. Astron. Soc.494(4), 6072 (2020)

  • [30]

    L. F. Wang, J. H. Zhang, D. Z. Heet al., Mon. Not. Roy. Astron. Soc.514(1), 1433 (2022)

  • [31]

    M. Millonet al., Astron. Astrophys.639, A101 (2020)

  • [32]

    S. Birreret al., Astron. Astrophys.643, A165 (2020)

  • [33]

    T. Collett, F. Montanari, and S. Rasanen, Phys. Rev. Lett.123(23), 231101 (2019)

  • [34]

    K. Liao, A. Shafieloo, R. E. Keeleyet al., Astrophys. J. Lett.886(1), L23 (2019)

  • [35]

    K. Liao, A. Shafieloo, R. E. Keeleyet al., Astrophys. J. Lett.895(2), L29 (2020)

  • [36]

    C. Escamilla-Rivera, M. A. C. Quintero, and S. Capozziello, JCAP2020(03), 008 (2020)

  • [37]

    L. Tang, X. Li, H. N. Linet al., Astrophys. J.907(2), 121 (2021)

  • [38]

    L. Liu, L. J. Hu, L. Tanget al., Res. Astron. Astrophys.23(12), 125012 (2023)

  • [39]

    J. Z. Qi, P. Meng, J. F. Zhanget al., Phys. Rev. D108(6), 063522 (2023)

  • [40]

    D. M. Scolnicet al., Astrophys. J.859(2), 101 (2018)

  • [41]

    S. Refsdal, Mon. Not. Roy. Astron. Soc.128(4), 307 (1964)

  • [42]

    M. Bartelmann and P. Schneider, Phys. Rept.340, 291 (2001)

  • [43]

    L. Tang, H. N. Lin, and Y. Wu, Chin. Phys. C49, 015104 (2025)

  • [44]

    D. Scolnicet al., Astrophys. J.938(2), 113 (2022)

  • [45]

    Y. Gal and Z. Ghahramani,Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, arXiv: 1506.02142

  • [46]

    G. J. Wang, X. J. Ma, S. Y. Liet al., Astrophys. J. Suppl.246(1), 13 (2020)

  • [47]

    F. Pedregosa, G. Varoquaux, A. Gramfortet al., Journal of Machine Learning Research12, 2825 (2011)

  • [48]

    D. Foreman-Mackey, D. W. Hogg, D. Langet al., Publ. Astron. Soc. Pac.125, 306 (2013)

  • [49]

    X. Li, R. E. Keeley, A. Shafielooet al., Astrophys. J.960(2), 103 (2024)

  • [50]

    M. Oguri and P. J. Marshall, Mon. Not. Roy. Astron. Soc.405, 2579 (2010)

Baidu
map