Model-independent determination of H0 and ΩK, 0 using time-delay galaxy lenses and gamma-ray bursts

Abstract

ABSTRACT Combining the ‘time-delay distance’ (DΔt) measurements from galaxy lenses and other distance indicators provides model-independent determinations of the Hubble constant (H0) and spatial curvature (ΩK, 0), only based on the validity of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and geometrical optics. To take the full merit of combining DΔt 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 ΩK, 0 is not improved due to the degeneracy between SN Ia absolute magnitude, MB, 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 MB–H0 degeneracy in SN Ia distances and ameliorate the restrictions on cosmographic parameters along with ΩK, 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.