Cosmological model insensitivity of local $H_0$ from the Cepheid distance ladder

The observed tension ($\sim 9\%$ difference) between the local distance ladder measurement of the Hubble constant, $H_0$, and its value inferred from the cosmic microwave background (CMB) could hint at new, exotic, cosmological physics. We test the impact of the assumption about the expansion history of the universe ($0.01<z<2.3$) on the local distance ladder estimate of $H_0$. In the fiducial analysis, the Hubble flow Type Ia supernova (SN~Ia) sample is truncated to $z < 0.15$ and the deceleration parameter ($q_0$) fixed to -0.55. We create realistic simulations of the calibrator and Pantheon samples and account for a full systematics covariance between these two sets. We fit several physically motivated dark energy models and derive combined constraints from calibrator and Pantheon SNe~Ia and simultaneously infer $H_0$ and dark energy properties. We find that the assumption on the dark energy model does not significantly change the local distance ladder value of $H_0$, with a maximum difference ($\Delta H_0$) between the inferred value for different models of 0.47 km$^{-1}$ s$^{-1}$ Mpc $^{-1}$, i.e. a 0.6$\%$ shift in $H_0$, significantly smaller than the observed tension. Additional freedom in the dark energy models does not increase the error in the inferred value of $H_0$. Including systematics covariance between the calibrators, low redshift SNe, and high redshift SNe can induce small shifts in the inferred value for $H_0$. The SN~Ia systematics in this study contribute $\lesssim 0.8 \%$ to the total uncertainty on $H_0$.