A redshift tomography of the Pantheon type Ia supernovae (SnIa) data focusing on the best fit value of the absolute magnitude $M$ and/or Hubble constant $H_0$ in the context of $\mathrm{\Lambda }\mathrm{CDM}$ indicates a local variation ($z\lesssim 0.2$) at $2\sigma$ level, with respect to the best fit of the full dataset. If this variation is not due to a statistical fluctuation, it can be interpreted as a locally higher value of $H_0$ by about 2%, corresponding to a local matter underdensity $\delta {\rho }_0/{\rho }_0\simeq -0.10\pm 0.04$. It can also be interpreted as a time variation of Newton’s constant which implies an evolving Chandrasekhar mass and thus an evolving absolute luminosity $L$ and absolute magnitude $M$ of low $z$ SnIa. The local void scenario would predict a degree of anisotropy in the best fit value of $H_0$ since it is unlikely that we are located at the center of a local spherical underdensity. Using a hemisphere comparison method, we find an anisotropy level that is consistent with simulated isotropic Pantheon-like datasets. We show however, that the anisotropic sky distribution of the Pantheon SnIa data induces a preferred range of directions even in simulated Pantheon data obtained in the context of isotropic $\mathrm{\Lambda }\mathrm{CDM}$. We thus construct a more isotropically distributed subset of the Pantheon SnIa and show that the preferred range of directions disappears. Using this more isotropically distributed subset we again find no evidence for statistically significant anisotropy using either the hemisphere comparison method or the dipole fit method. In the context of the modified gravity scenario, we allow for an evolving normalized Newton’s constant consistent with general relativity (GR) at early and late times $\mu (z)=G_{\mathrm{eff}}(z,g_a)/G_{\mathrm{N}}=1+g_a{z}^2/(1+z{)}^2-g_a{z}^4/(1+z{)}^4$ and fit for the parameter $g_a$ assuming $L\sim G_{\mathrm{eff}}^b$. For $b=-3/2$ indicated by some previous studies we find $g_a=-0.47\pm 0.36$ which is more than $1.5\sigma$ away from the GR value of $g_a=0$. This weak hint for weaker gravity at low $z$ coming from SnIa is consistent with similar evidence from growth and weak lensing cosmological data.

• Received 24 April 2020
• Accepted 26 June 2020

DOI:https://doi.org/10.1103/PhysRevD.102.023520