  The standard cosmological model assumes a homogeneous and isotropic universe
as the background spacetime on large scales called the cosmological principle.
However, some observations suggest the possibility of an inhomogeneous and
anisotropic universe at large scales. In this paper, we investigate a model of
the universe with random inhomogeneities and anisotropies on very large scales,
motivated by the supercurvature dark energy model in Nan et al. [Phys. Rev. D
99, 103512 (2019)]. In this model, the authors introduced a scalar field with
$\mathcal{O}(1)$ inhomogeneities on a scale sufficiently larger than the
current horizon scale (superhorizon scale), and the potential energy of the
scalar field explains the accelerating expansion, with slight deviations from
the cosmological principle. We aim at clarifying the theoretical prediction on
the large-scale structure (LSS) of the matter component in this model. Based on
the work on the superhorizon scale fluctuations (superhorizon mode) presented
in Nan and Yamamoto [Phys. Rev. D 105, 063518 (2022)], we derive the equations
that the perturbative components to the LSS obey as a generalization of the
cosmological perturbations theory, which is solved to find the influence of the
dark energy inhomogeneities on the formation of the LSS. Finally, we show that
the model can be consistent with observations by comparing the $\sigma_8$
predicted by the numerical solution of the model with the $\sigma_8$ indicated
by observations such as Planck and SDSS.
