  There are many possibilities of scenarios in the early universe, which can
give rise to the same observational signals due to the degeneracy among each
other, caused by equivalence under the conformal transformations. In order to
break the degeneracy, in this paper we take into account the so-called
"frame-invariant variables" proposed by A. Ijjas and P. J. Steinhardt in
\cite{Ijjas:2015zma}. We discuss how the different scenarios will distribute in
different parametric space constructed from those variables, waiting for the
judgement of real observations in the future. Several concrete models with
explicit non-minimal coupling functions are also discussed.
