Table 3.
Open in new tab

Best-fitting values for cosmological parameters |$\sigma _{8}$|⁠, |$\Omega _{m}$|⁠, |$H_0$|⁠, and n for both |$\Lambda$|CDM and |$f(Q)$|-gravity power-law models using |$f\sigma {_8}$|⁠, |$\sigma _8+f$|⁠, |$\sigma _8+f\, +\, f\sigma _8$|⁠, OHD + SNIa  + |$f\sigma _8$|⁠, OHD + SNIa  + |$\sigma _8+f$| and OHD + SNIa  + |$\sigma _8+f\, +\, f\sigma _8$|⁠. The CMB Planck-2018 value for the matter fluctuation amplitude (⁠|$\sigma _8)$| is |$\sigma _8 = 0.811\pm 0.006$| (Aghanim et al. 2020).

Parameters|$\Omega _m$||$\sigma _{8}$|n|$H_0$|
    |$(\rm km\, s^{-1}Mpc^{-1})$|
|$\Lambda$|CDM    
|$f\sigma _8$||$0.288^{+0.023}_{-0.022}$||$0.806^{+0.019}_{-0.018}$|––
|$\sigma _8+f$||$0.278^{+0.004}_{0.004}$||$0.780^{+0.009}_{0.009}$|––
|$\sigma _8 + f + f\sigma _8$||$0.290^{+0.009}_{0.009}$||$0.790^{+0.013}_{-0.013}$|––
OHD + SNIa  + |$f\sigma _8$||$0.323^{+0.009}_{-0.009}$||$0.800^{+0.015}_{-0.015}$|–|$73.09^{+0.60}_{-0.60}$|
OHD + SNIa  + |$\sigma _8+f$||$0.321^{+0.007}_{-0.007}$||$0.815^{+0.011}_{-0.011}$|–|$73.43^{+0.82}_{-0.75}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.336^{+0.007}_{-0.007}$||$0.801^{+0.008}_{-0.008}$|–|$72.94^{+0.17}_{-0.19}$|
|$f(Q)$| model    
|$f\sigma _8$||$0.300^{+0.037}_{-0.022}$||$0.792^{+0.012}_{-0.012}$||$0.090^{+0.035}_{-0.012}$|–
|$\sigma _8+f$||$0.275^{+0.020}_{-0.065}$||$0.774^{+0.009}_{0.009}$||$-0.120^{+0.013}_{-0.011}$|–
|$\sigma _8+f+f\sigma _8$||$0.282^{+0.033}_{-0.021}$||$0.785^{+0.012}_{-0.012}$||$0.100^{+0.034}_{-0.011}$|–
OHD + SNIa  + |$f\sigma _8$||$0.335^{+0.058}_{-0.051}$||$0.809^{+0.012}_{-0.019}$||$-0.01^{+0.019}_{-0.018}$||$72.75^{+2.20}_{-2.50}$|
OHD + SNIa  + |$\sigma _8+f$||$0.320^{+0.047}_{-0.039}$||$0.821^{+0.034}_{-0.034}$||$-0.013^{+0.010}_{-0.009}$||$73.32^{+2.70}_{-3.90}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.327^{+0.056}_{-0.045}$||$0.826^{+0.026}_{-0.037}$||$-0.025^{+0.021}_{-0.010}$||$72.41^{+2.40}_{-3.10}$|
Parameters|$\Omega _m$||$\sigma _{8}$|n|$H_0$|
    |$(\rm km\, s^{-1}Mpc^{-1})$|
|$\Lambda$|CDM    
|$f\sigma _8$||$0.288^{+0.023}_{-0.022}$||$0.806^{+0.019}_{-0.018}$|––
|$\sigma _8+f$||$0.278^{+0.004}_{0.004}$||$0.780^{+0.009}_{0.009}$|––
|$\sigma _8 + f + f\sigma _8$||$0.290^{+0.009}_{0.009}$||$0.790^{+0.013}_{-0.013}$|––
OHD + SNIa  + |$f\sigma _8$||$0.323^{+0.009}_{-0.009}$||$0.800^{+0.015}_{-0.015}$|–|$73.09^{+0.60}_{-0.60}$|
OHD + SNIa  + |$\sigma _8+f$||$0.321^{+0.007}_{-0.007}$||$0.815^{+0.011}_{-0.011}$|–|$73.43^{+0.82}_{-0.75}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.336^{+0.007}_{-0.007}$||$0.801^{+0.008}_{-0.008}$|–|$72.94^{+0.17}_{-0.19}$|
|$f(Q)$| model    
|$f\sigma _8$||$0.300^{+0.037}_{-0.022}$||$0.792^{+0.012}_{-0.012}$||$0.090^{+0.035}_{-0.012}$|–
|$\sigma _8+f$||$0.275^{+0.020}_{-0.065}$||$0.774^{+0.009}_{0.009}$||$-0.120^{+0.013}_{-0.011}$|–
|$\sigma _8+f+f\sigma _8$||$0.282^{+0.033}_{-0.021}$||$0.785^{+0.012}_{-0.012}$||$0.100^{+0.034}_{-0.011}$|–
OHD + SNIa  + |$f\sigma _8$||$0.335^{+0.058}_{-0.051}$||$0.809^{+0.012}_{-0.019}$||$-0.01^{+0.019}_{-0.018}$||$72.75^{+2.20}_{-2.50}$|
OHD + SNIa  + |$\sigma _8+f$||$0.320^{+0.047}_{-0.039}$||$0.821^{+0.034}_{-0.034}$||$-0.013^{+0.010}_{-0.009}$||$73.32^{+2.70}_{-3.90}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.327^{+0.056}_{-0.045}$||$0.826^{+0.026}_{-0.037}$||$-0.025^{+0.021}_{-0.010}$||$72.41^{+2.40}_{-3.10}$|
Table 3.
Open in new tab

Best-fitting values for cosmological parameters |$\sigma _{8}$|⁠, |$\Omega _{m}$|⁠, |$H_0$|⁠, and n for both |$\Lambda$|CDM and |$f(Q)$|-gravity power-law models using |$f\sigma {_8}$|⁠, |$\sigma _8+f$|⁠, |$\sigma _8+f\, +\, f\sigma _8$|⁠, OHD + SNIa  + |$f\sigma _8$|⁠, OHD + SNIa  + |$\sigma _8+f$| and OHD + SNIa  + |$\sigma _8+f\, +\, f\sigma _8$|⁠. The CMB Planck-2018 value for the matter fluctuation amplitude (⁠|$\sigma _8)$| is |$\sigma _8 = 0.811\pm 0.006$| (Aghanim et al. 2020).

Parameters|$\Omega _m$||$\sigma _{8}$|n|$H_0$|
    |$(\rm km\, s^{-1}Mpc^{-1})$|
|$\Lambda$|CDM    
|$f\sigma _8$||$0.288^{+0.023}_{-0.022}$||$0.806^{+0.019}_{-0.018}$|––
|$\sigma _8+f$||$0.278^{+0.004}_{0.004}$||$0.780^{+0.009}_{0.009}$|––
|$\sigma _8 + f + f\sigma _8$||$0.290^{+0.009}_{0.009}$||$0.790^{+0.013}_{-0.013}$|––
OHD + SNIa  + |$f\sigma _8$||$0.323^{+0.009}_{-0.009}$||$0.800^{+0.015}_{-0.015}$|–|$73.09^{+0.60}_{-0.60}$|
OHD + SNIa  + |$\sigma _8+f$||$0.321^{+0.007}_{-0.007}$||$0.815^{+0.011}_{-0.011}$|–|$73.43^{+0.82}_{-0.75}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.336^{+0.007}_{-0.007}$||$0.801^{+0.008}_{-0.008}$|–|$72.94^{+0.17}_{-0.19}$|
|$f(Q)$| model    
|$f\sigma _8$||$0.300^{+0.037}_{-0.022}$||$0.792^{+0.012}_{-0.012}$||$0.090^{+0.035}_{-0.012}$|–
|$\sigma _8+f$||$0.275^{+0.020}_{-0.065}$||$0.774^{+0.009}_{0.009}$||$-0.120^{+0.013}_{-0.011}$|–
|$\sigma _8+f+f\sigma _8$||$0.282^{+0.033}_{-0.021}$||$0.785^{+0.012}_{-0.012}$||$0.100^{+0.034}_{-0.011}$|–
OHD + SNIa  + |$f\sigma _8$||$0.335^{+0.058}_{-0.051}$||$0.809^{+0.012}_{-0.019}$||$-0.01^{+0.019}_{-0.018}$||$72.75^{+2.20}_{-2.50}$|
OHD + SNIa  + |$\sigma _8+f$||$0.320^{+0.047}_{-0.039}$||$0.821^{+0.034}_{-0.034}$||$-0.013^{+0.010}_{-0.009}$||$73.32^{+2.70}_{-3.90}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.327^{+0.056}_{-0.045}$||$0.826^{+0.026}_{-0.037}$||$-0.025^{+0.021}_{-0.010}$||$72.41^{+2.40}_{-3.10}$|
Parameters|$\Omega _m$||$\sigma _{8}$|n|$H_0$|
    |$(\rm km\, s^{-1}Mpc^{-1})$|
|$\Lambda$|CDM    
|$f\sigma _8$||$0.288^{+0.023}_{-0.022}$||$0.806^{+0.019}_{-0.018}$|––
|$\sigma _8+f$||$0.278^{+0.004}_{0.004}$||$0.780^{+0.009}_{0.009}$|––
|$\sigma _8 + f + f\sigma _8$||$0.290^{+0.009}_{0.009}$||$0.790^{+0.013}_{-0.013}$|––
OHD + SNIa  + |$f\sigma _8$||$0.323^{+0.009}_{-0.009}$||$0.800^{+0.015}_{-0.015}$|–|$73.09^{+0.60}_{-0.60}$|
OHD + SNIa  + |$\sigma _8+f$||$0.321^{+0.007}_{-0.007}$||$0.815^{+0.011}_{-0.011}$|–|$73.43^{+0.82}_{-0.75}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.336^{+0.007}_{-0.007}$||$0.801^{+0.008}_{-0.008}$|–|$72.94^{+0.17}_{-0.19}$|
|$f(Q)$| model    
|$f\sigma _8$||$0.300^{+0.037}_{-0.022}$||$0.792^{+0.012}_{-0.012}$||$0.090^{+0.035}_{-0.012}$|–
|$\sigma _8+f$||$0.275^{+0.020}_{-0.065}$||$0.774^{+0.009}_{0.009}$||$-0.120^{+0.013}_{-0.011}$|–
|$\sigma _8+f+f\sigma _8$||$0.282^{+0.033}_{-0.021}$||$0.785^{+0.012}_{-0.012}$||$0.100^{+0.034}_{-0.011}$|–
OHD + SNIa  + |$f\sigma _8$||$0.335^{+0.058}_{-0.051}$||$0.809^{+0.012}_{-0.019}$||$-0.01^{+0.019}_{-0.018}$||$72.75^{+2.20}_{-2.50}$|
OHD + SNIa  + |$\sigma _8+f$||$0.320^{+0.047}_{-0.039}$||$0.821^{+0.034}_{-0.034}$||$-0.013^{+0.010}_{-0.009}$||$73.32^{+2.70}_{-3.90}$|
OHD + SNIa  + |$\sigma _8+f+f\sigma _8$||$0.327^{+0.056}_{-0.045}$||$0.826^{+0.026}_{-0.037}$||$-0.025^{+0.021}_{-0.010}$||$72.41^{+2.40}_{-3.10}$|
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