  Future galaxy redshift surveys aim at probing the clustering of the cosmic
large-scale structure with unprecedented accuracy, thus complementing cosmic
microwave background experiments in the quest to deliver the most precise and
accurate picture ever of our Universe. Analyses of such measurements are
usually performed within the context of the so-called vanilla LCDM model - the
six-parameter phenomenological model which, for instance, emerges from best
fits against the recent data obtained by the Planck satellite. Here, we show
that such an approach is prone to subtle systematics when the Gaussianity of
primordial fluctuations is concerned. In particular, we demonstrate that, if we
neglect even a tiny amount of primordial non-Gaussianity - fully consistent
with current limits - we shall introduce spurious biases in the reconstruction
of cosmological parameters. This is a serious issue that must be properly
accounted for in view of accurate (as well as precise) cosmology.
