Dark energy, integrated Sachs-Wolfe effect and large-scale magnetic fields

The impact of large-scale magnetic fields on the interplay between the ordinary and integrated Sachs-Wolfe effects is investigated in the presence of a fluctuating dark energy component. The modified initial conditions of the Einstein-Boltzmann hierarchy allow for the simultaneous inclusion of dark energy perturbations and of large-scale magnetic fields. The temperature and polarization angular power spectra are compared with the results obtained in the magnetized version of the (minimal) concordance model. Purported compensation effects arising at large scales are specifically investigated. The fluctuating dark energy component modifies, in a computable manner, the shapes of the 1- and 2-$\sigma$ contours in the parameter space of the magnetized background. The allowed spectral indices and magnetic field intensities turn out to be slightly larger than those determined in the framework of the magnetized concordance model where the dark energy fluctuations are absent.