Isocurvature modes and Baryon Acoustic Oscillations II: gains from
  combining CMB and Large Scale Structure
  We consider cosmological parameters estimation in the presence of a non-zero
isocurvature contribution in the primordial perturbations. A previous analysis
showed that even a tiny amount of isocurvature perturbation, if not accounted
for, could affect standard rulers calibration from Cosmic Microwave Background
observations such as those provided by the Planck mission, affect Baryon
Acoustic Oscillations interpretation and introduce biases in the recovered dark
energy properties that are larger than forecasted statistical errors from
future surveys. Extending on this work, here we adopt a general fiducial
cosmology which includes a varying dark energy equation of state parameter and
curvature. Beside Baryon Acoustic Oscillations measurements, we include the
information from the shape of the galaxy power spectrum and consider a joint
analysis of a Planck-like Cosmic Microwave Background probe and a future,
space-based, Large Scale Structure probe not too dissimilar from recently
proposed surveys. We find that this allows one to break the degeneracies that
affect the Cosmic Microwave Background and Baryon Acoustic Oscillations
combination. As a result, most of the cosmological parameter systematic biases
arising from an incorrect assumption on the isocurvature fraction parameter
$f_{iso}$, become negligible with respect to the statistical errors. We find
that the Cosmic Microwave Background and Large Scale Structure combination
gives a statistical error $\sigma(f_{iso}) \sim 0.008$, even when curvature and
a varying dark energy equation of state are included, which is smaller than the
error obtained from Cosmic Microwave Background alone when flatness and
cosmological constant are assumed. These results confirm the synergy and
complementarity between Cosmic Microwave Background and Large Scale Structure,
and the great potential of future and planned galaxy surveys.
