  Dark energy has been introduced to explain the present accelerating expansion
of the universe. In the LambdaCDM model, the present standard model of
cosmology, dark energy is described as a cosmological constant which is time
independent. The possibility of the time dependence of dark energy has been
investigated to obtain deeper understanding of it by looking redshit-magnitude
relation of type Ia supernova, for example. We investigate the constraints to
the time dependence of dark energy with several phenomenological models by
fitting their parameters to the redshit-magnitude relation of the Pantheon
supernova catalog, and confirm that little time dependence can not be excluded
by the goodness-of-fit criterion only. Such a non-trivial time dependence
causes different expansion rate in the period of reionization, which affects
the low-l polarization power spectrum of CMB. We investigate the possibility to
detect the effect in future probe like LiteBIRD, for example. We find that the
low-l EE polarization power spectrum is enhanced in general, but it will be
difficult to be detected as far as looking the EE polarization power spectrum
only because of the limitation by cosmic variance.
