Comparing Hemispheres: Anisotropy in the deceleration parameter $q_0$

Abstract

We present a hemispherical comparison analysis of the deceleration parameter $q_0$ using the Pantheon+ sample of Type Ia supernovae to test the isotropy of cosmic acceleration and the robustness of redshift corrections. We detect directional variations in $q_0$ across redshift frames. Even in the $z_{\mathrm{HD}}$ frame, where corrections for the CMB dipole and peculiar velocities are applied, a residual dipolar anisotropy persists with $\Delta q_0 = 0.112$ and a maximum signal to noise $S/N = 2.155$, aligned with the CMB dipole direction and decreasing with increasing minimum redshift cut. The anisotropy is stronger in the $z_{\mathrm{hel}}$ and $z_{\mathrm{CMB}}$ frames, where kinematic corrections are incomplete, while the transition to $z_{\mathrm{HD}}$ reduces but does not remove the signal. Inferring the dipole from the supernovae data yields $v_{\odot} = 307.26^{+32.00}_{-22.28},\mathrm{km \, s^{-1}}$ toward $(\mathrm{RA},\mathrm{DEC}) = (156.40^{+4.72}_{-4.71}, -3.38^{+5.54}_{-8.23})^\circ$, mildly discrepant with the Planck CMB dipole at the $\sim 1.9\sigma$ level. When this SNe inferred dipole is incorporated into the redshift correction pipeline, the hemispherical anisotropy is suppressed, with the dipolar pattern disappearing and the maximum signal reduced to $S/N \lesssim 1.75$, while the remaining fluctuations become consistent with statistical noise, suggesting that part of the signal arises from residual mismatches in the modeling of the local velocity field. Since current redshift corrections rely on peculiar velocity reconstructions based on the density field, our results suggest a residual bulk flow not fully captured by these models, highlighting a source of systematic uncertainty in low redshift supernova cosmology.