Towards degeneracy breaking of early universe models

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.