A Uniform Type Ia Supernova Distance Ladder with the Zwicky Transient Facility: Absolute Calibration Based on the Tip of the Red Giant Branch (TRGB) Method

The current Cepheid-calibrated distance ladder measurement of $H_0$ is reported to be in tension with the values inferred from the cosmic microwave background (CMB), assuming standard cosmology. However, some tip of the red giant branch (TRGB) estimates report $H_0$ in better agreement with the CMB. Hence, it is critical to reduce systematic uncertainties in local measurements to understand the Hubble tension. In this paper, we propose a uniform distance ladder between the second and third rungs, combining SNe~Ia observed by the Zwicky Transient Facility (ZTF) with a TRGB calibration of their absolute luminosity. A large, volume-limited sample of both calibrator and Hubble flow SNe~Ia from the \emph{same} survey minimizes two of the largest sources of systematics: host-galaxy bias and non-uniform photometric calibration. We present results from a pilot study using existing TRGB distance to the host galaxy of ZTF SN~Ia SN 2021rhu (aka ZTF21abiuvdk) in NGC7814. Combining the ZTF calibrator with a volume-limited sample from the first data release of ZTF Hubble flow SNe~Ia, we infer $H_0 = 76.94 \pm 6.4\, {\rm km}\,{\rm s^{-1}}\,{\rm Mpc^{-1}}$, an $8.3 \%$ measurement. The error budget is dominated by the single object calibrating the SN~Ia luminosity in this pilot study. However, the ZTF sample includes already five other SNe~Ia within $\sim$ 20 Mpc for which TRGB distances can be obtained with HST. Finally, we present the prospects of building this distance ladder out to 80 Mpc with JWST observations of more than one hundred ZTF SNe~Ia.