Study On Duality Of Cosmological Models

Although there are many cosmological models of the early universe that have obtained a scale-invariant scalar perturbation power spectrum consistent with the observations,we still don't know which model truly describes our universe.Because of the different principles for their realization,different models of the early universe describe different evolutionary processes of the early universe,which means that they have different scale factor evolution processes,and different the equation of state and the different sound speed of perturbation waves in theory.So we parameterize the sound speed of perturbation waves cs?(-?s)and slow-roll parameter(?)?(-??).Then when the condition that the power spectrum is scale invariant is satisfied,different approximation of slow-roll parameter(?)resulting in different relations of ?and s.When ? and s take specific values,several currently known models and some possible new models can be obtained separately.It proves that there is a theoretical duality in the evolution of the early universe dominated by different materials,in the other words,the equivalence of different background processes but the same observation results.