CMB power spectra induced by primordial cross-bispectra between metric
  perturbations and vector fields
  We study temperature and polarization anisotropies of the cosmic microwave
background (CMB) radiation sourced from primordial cross-bispectra between
metric perturbations and vector fields, which are generated from the inflation
model where an inflaton and a vector field are coupled. In case the vector
field survives after the reheating, both the primordial scalar and tensor
fluctuations can be enhanced by the anisotropic stress composed of the vector
fields during radiation dominated era. We show that through this enhancement
the primordial cross-bispectra generate not only CMB bispectra but also CMB
power spectra. In general, we can expect such cross-bispectra produce the
non-trivial mode-coupling signals between the scalar and tensor fluctuations.
However, we explicitly show that such mode-coupling signals do not appear in
CMB power spectra. Through the numerical analysis of the CMB scalar-mode power
spectra, we find that although signals from these cross-bispectra are smaller
than primary non-electromagnetic ones, these have some characteristic features
such as negative auto-correlations of the temperature and polarization modes,
respectively. On the other hand, signals from tensor modes are almost
comparable to primary non-electromagnetic ones and hence the shape of observed
$B$-mode spectrum may deviate from the prediction in the non-electromagnetic
case. The above imprints may help us to judge the existence of the coupling
between the scalar and vector fields in the early Universe.
