  We consider a dynamical model for dark energy based on an ultralight mass
scalar field with very large-scale inhomogeneities. This model may cause
observable impacts on the anisotropic properties of the cosmic microwave
background (CMB) intensity and luminosity distance. We formulate the model as
the cosmological perturbations of the superhorizon scales, focusing on the
local region of our universe. Moreover, we investigated the characteristic
properties of the late-time evolution of inhomogeneous dark energy. Our
numerical solutions show that the model can mimic the standard $\Lambda$CDM
cosmology while including spatially dependent dark energy with flexible ranges
of the model parameters. We put a constraint on the amplitude of these
inhomogeneities of the dark energy on very large scales with the observations
of the CMB anisotropies. We also discuss their influence on the estimation of
the luminosity distance.
