Reconstructing a large-scale matter-density contrast profile to reconcile Pantheon + supernovae with DESI DR2 BAO observations in an inhomogeneous universe

The Hubble parameters measured by the DESI DR2 BAO observations show a significant discrepancy from the prediction of the standard cosmological model. This discrepancy, together with the long-discussed Hubble tension, may originate from large-scale inhomogeneities in the matter distribution. This interpretation is motivated by infrared galaxy surveys, which suggest that our galaxy resides within the $\sim300$ Mpc under-dense region known as the KBC void. In this study, we apply a linear order relation -- relating the horizon-scale Hubble parameter inferred from CMB observations and the local-scale Hubble parameter -- to the Pantheon+ Type Ia supernovae and the DESI DR2 BAO data. We show that a simple inhomogeneous cosmological model consisting of eight top-hat shells can consistently explain the Hubble parameters inferred from both observations. Based on the matter-density distribution, we also briefly discuss its possible impact on cosmological observables, including the magnitude--redshift relation, the kinematic Sunyaev--Zel'dovich effect, and the integrated Sachs--Wolfe effect.