  The form of the primordial power spectrum (PPS) of cosmological scalar
(matter density) perturbations is not yet constrained satisfactorily in spite
of the tremendous amount of information from the Cosmic Microwave Background
(CMB) data. While a smooth power-law-like form of the PPS is consistent with
the CMB data, some PPS with small non-smooth features at large scales can also
fit the CMB temperature and polarization data with similar statistical
evidence. Future CMB surveys cannot help distinguish all such models due to the
cosmic variance at large angular scales. In this paper, we study how well we
can differentiate be- tween such featured forms of the PPS not otherwise
distinguishable using CMB data. We ran 15 N-body DESI-like simulations of these
models to explore this approach. Showing that statistics such as the halo mass
function and the two-point correlation function are not able to distinguish
these models in a DESI-like survey, we advocate to avoid reducing the
dimensionality of the problem by demonstrating that the use of a simple
three-dimensional count-in-cell density field can be much more effective for
the purpose of model distinction.
