# Local determination of the Hubble constant and the deceleration parameter

## TL;DR

This paper refines local measurements of the Hubble constant using supernova data, finding results that significantly differ from Planck CMB estimates and providing new insights into cosmic acceleration.

## Contribution

It introduces an effective calibration prior for supernova absolute magnitude and derives a local Hubble constant independent of the standard $
m{ extLambda}$CDM model assumptions.

## Key findings

- H_0 = 75.35 ± 1.68 km s^{-1} Mpc^{-1} with 2.2% uncertainty
- H_0 is in 4.5σ tension with Planck results
- Deceleration parameter q_0 = -1.08 ± 0.29, differing from Planck

## Abstract

The determination of the Hubble constant $H_0$ from the Cosmic Microwave Background by the Planck Collaboration [Aghanim et al. 2018] is in tension at $4.2\sigma$ with respect to the local determination of $H_0$ by the SH0ES collaboration [Reid et al. 2019]. Here, we improve upon the local determination, which fixes the deceleration parameter to the standard $\Lambda$CDM model value of $q_0=-0.55$, that is, uses information from observations beyond the local universe. First, we derive the effective calibration prior on the absolute magnitude $M_B$ of Supernovae Ia, which can be used in cosmological analyses in order to avoid the double counting of low-redshift supernovae. We find $M_B = -19.2334 \pm 0.0404$ mag. Then, we use the above $M_B$ prior in order to obtain a determination of the local $H_0$ which only uses local observations and only assumes the cosmological principle, that is, large-scale homogeneity and isotropy. This is achieved by adopting an uninformative flat prior for $q_0$ in the cosmographic expansion of the luminosity distance. We use the latest Pantheon sample and find $H_0= 75.35 \pm 1.68 \text{ km s}^{-1} {\rm Mpc}^{-1}$, which features a 2.2% uncertainty, close to the 1.9% error obtained by the SH0ES Collaboration. Our determination is at the higher tension of $4.5\sigma$ with the latest results from the Planck Collaboration that assume the $\Lambda$CDM model. Furthermore, we also constrain the deceleration parameter to $q_0= -1.08 \pm 0.29$, which disagrees with Planck at the $1.9\sigma$ level. These estimations only use supernovae in the redshift range $0.023\le z\le 0.15$.