  We study observational consequences of the model for dark energy proposed in
[1] (Aoki et al., Phys.Rev. D97 (2018) no.4, 043517). We assume our universe
has been created by bubble nucleation, and consider quantum fluctuations of an
ultralight scalar field. Residual effects of fluctuations generated in an
ancestor vacuum (de Sitter space in which the bubble was formed) is interpreted
as dark energy. Its equation of state parameter w(z) has a characteristic form,
approaching -1 in the future, but -1/3 in the past. A novel feature of our
model is that dark energy effectively increases the magnitude of the negative
spatial curvature in the evolution of the Hubble parameter, though it does not
alter the definition of the angular diameter distance. We perform Fisher
analysis and forecast the constraints for our model from future galaxy surveys
by Square Kilometre Array and Euclid. Due to degeneracy between dark energy and
the spatial curvature, galaxy surveys alone can determine these parameters only
for optimistic choices of their values, but combination with other independent
observations, such as CMB, will greatly improve the chance of determining them.
