Testing the Hubble law with Pantheon+

The Hubble law (HL) governs the low-redshift (low-z) evolution of the distance of an object. However, there is a lack of an investigation of its validity and effective radius for a long time, since the low-z background data with a high precision is scarce. The latest Type Ia supernovae sample Pantheon+ having a significant increase of low-z data provides an excellent opportunity to test the HL. We propose a generalized HL and implement the first modern test of the HL with Pantheon+. We obtain the constraint on the deviation parameter $\alpha=1.00118\pm0.00044$, confirm the validity of linear HL with a $0.04\%$ precision and give the transition redshift $z_t=0.03$ and luminosity distance $D_{L,t}=123.13\pm1.75$ Mpc, which means that HL holds when $z<0.03$ and breaks down at a distance of $D_L>123.13$ Mpc. Comparing the ability of Type Ia supernovae and HII galaxies in testing the HL, we stress the uniqueness and strong power of Type Ia supernovae in probing the low-z physics.