In this talk, we will discuss the relevance of various parametrizations
of Cosmic Inflation recently introduced as an attempt to simplify and
unify inflationary observable predictions. Typically, they involve two
parameters associated with an expansion of the inflationary quantities
matching the belief that inflation is characterized by two numbers only,
the tensor-to-scalar ratio and the scalar spectral index. Restricting
ourselves to the cases in which these expansions can be made
mathematically consistent,
we give different arguments and examples showing that they are either
not generic or insufficient to make predictions at the accuracy level
needed by the cosmological data.