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Spherically symmetric dust universe models with a positive cosmologicalconstant $\Lambda$, known as $\Lambda$-Lema\^itre-Tolman-Bondi($\Lambda$LTB)models, are considered. We report a method to construct the $\Lambda$LTB modelfrom a given distance-redshift relation observed at the symmetry center. Thespherical inhomogeneity is assumed to be composed of growing modes. We derive aset of ordinary differential equations for three functions of the redshift,which specify the spherical inhomogeneity. Once a distance-redshift relation isgiven, with careful treatment of possible singular points, we can uniquelydetermine the model by solving the differential equations for each value of$\Lambda$. As a demonstration, we fix the distance-redshift relation as that ofthe flat $\Lambda$CDM model with $(\Omega^{\rm dis}_{\rm m0}, \Omega^{\rmdis}_{\rm \Lambda 0})=(0.3,0.7)$, where $\Omega^{\rm dis}_{\rm m0}$ and$\Omega^{\rm dis}_{\rm \Lambda 0}$ are the normalized matter density and thecosmological constant, respectively. Then, we construct the $\Lambda$LTB modelfor several values of $\Omega_{\rm \Lambda 0}:=\Lambda/(3H_0^2)$, where $H_0$is the present Hubble parameter observed at the symmetry center. We obtain voidstructure around the symmetry center for $\Omega_{\Lambda 0}<\Omega^{\rmdis}_{\Lambda 0}$. We show the relation between the ratio$\Omega_{\Lambda0}/\Omega^{\rm dis}_{\Lambda 0}$ and the amplitude of theinhomogeneity.

Inverse Construction of the $\Lambda$LTB Model from a Distance-redshift Relation