Polarization of CMB and possible time dependence of dark energy

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.