SIMBAD references

Combining the 'time-delay distance' (D_Δt) measurements from galaxy lenses and other distance indicators provides model-independent determinations of the Hubble constant (H₀) and spatial curvature (Ω_K, 0_), only based on the validity of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and geometrical optics. To take the full merit of combining D_Δt measurements in constraining H₀, we use gamma-ray burst (GRB) distances to extend the redshift coverage of lensing systems much higher than that of Type Ia Supernovae (SNe Ia) and even higher than quasars, whilst the general cosmography with a curvature component is implemented for the GRB distance parametrizations. Combining Lensing + GRB yields $H_0=71.5^{+4.4}_{-3.0}$ km s^–1 Mpc^–1 and $\Omega _{K,0} = -0.07^{+0.13}_{-0.06}$ (1σ). A flat-universe prior gives slightly an improved $H_0 = 70.9^{+4.2}_{-2.9}$ km s^–1Mpc^–1. When combining Lensing+GRB + SN Ia, the error bar ΔH₀ falls by 25 per cent, whereas Ω_K, 0_ is not improved due to the degeneracy between SN Ia absolute magnitude, M_B, and H₀ along with the mismatch between the SN Ia and GRB Hubble diagrams at z ≳ 1.4. Future increment of GRB observations can help to moderately eliminate the M_B-H₀ degeneracy in SN Ia distances and ameliorate the restrictions on cosmographic parameters along with Ω_K, 0_ when combining Lensing+SN Ia + GRB. We conclude that there is no evidence of significant deviation from a (an) flat (accelerating) universe and H₀ is currently determined at 3 per cent precision. The measurements show great potential to arbitrate the H₀ tension between the local distance ladder and cosmic microwave background measurements and provide a relevant consistency test of the FLRW metric.