Potential signature of a quadrupolar Hubble expansion in Pantheon+ supernovae

The assumption of isotropy -- that the Universe looks the same in all directions on large scales -- is fundamental to the standard cosmological model. This model forms the building blocks of essentially all of our cosmological knowledge to date. It is therefore critical to empirically test in which regimes its core assumptions hold. Anisotropies in the cosmic expansion are expected on small scales due to nonlinear structures in the late Universe, however, the extent to which these anisotropies might impact our low-redshift observations remains to be fully tested. In this paper, we use fully general relativistic simulations to calculate the expected local anisotropic expansion and identify the dominant multipoles in cosmological parameters to be the quadrupole in the Hubble parameter and the dipole in the deceleration parameter. We constrain these multipoles simultaneously in the new Pantheon+ supernova compilation. The fiducial analysis is done in the rest frame of the CMB with peculiar velocity corrections. Under the fiducial range of redshifts in the Hubble flow sample, we find a $\sim 2\sigma$ deviation from isotropy. We constrain the eigenvalues of the quadrupole in the Hubble parameter to be $\lambda_1 =0.021\pm{ 0.011}$ and $ {\lambda_2= 3.15\times 10^{-5}}\pm 0.012$ and place a $1\sigma$ upper limit on its amplitude of $2.88\%$. We find no significant dipole in the deceleration parameter, finding constraints of $q_{\rm dip} = 4.5^{+1.9}_{-5.4}$. However, in the rest frame of the CMB without corrections, we find $ q_{ \rm dip} = 9.6^{+4.0}_{-6.9}$, a $>2\sigma$ positive amplitude. We also investigate the impact of these anisotropies on the Hubble tension. We find a maximal shift of $0.30$ km s$^{-1}$ Mpc$^{-1}$ in the monopole of the Hubble parameter and conclude that local anisotropies are unlikely to fully explain the observed tension.