  The observables of the perturbed universe, CMB anisotropy and large
structures, depend on a set of cosmological parameters, as well as, the assumed
nature of primordial perturbations. In particular, the shape of the primordial
power spectrum (PPS) is, at best, a well motivated assumption. It is known that
the assumed functional form of the PPS in cosmological parameter estimation can
affect the best fit parameters and their relative confidence limits. In this
paper, we demonstrate that a specific assumed form actually drives the best fit
parameters into distinct basins of likelihood in the space of cosmological
parameters where the likelihood resists improvement via modifications to the
PPS. The regions where considerably better likelihoods are obtained allowing
free form PPS lie outside these basins. In the absence of a preferred model of
inflation, this raises a concern that current cosmological parameters estimates
are strongly prejudiced by the assumed form of PPS. Our results strongly
motivate approaches toward simultaneous estimation of the cosmological
parameters and the shape of the primordial spectrum from upcoming cosmological
data. It is equally important for theorists to keep an open mind towards early
universe scenarios that produce features in the PPS.
