Distinguishing Early Universe Scenarios With Scale-invariant Power Spectrum

As observational techniques have improved in recent decades,although infla-tion is accordant with the observation and is wildly accepted scenario of early u-niverse,inflation still has problems(such as singularities)that it cannot solve and there are still degeneracy with other early cosmological scenarios.This paper will find four different stages of early cosmology,namely inflation,matter contraction,slow contraction and slow expansion,from the condition that the scale invariance of pow-er spectrum is satisfied in the early cosmological stage.And then we construct some frame-invariant quantities and research their value ranges to get the different limit ranges of parameters.Finally we can distinguish them or reduce their degeneracies.We also start from the non-minimum coupling action in Jordan frame and use modify gravity theory to construct three parameterizations about f[?(t)].We rewrite the expressions of frame-invariant quantities and constrain parameters in f[?(t)]from viewpoint of theory.Finally maybe we can distinguish early cosmological scenarios.