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There have been thousands of cosmological models for our early universeproposed in the literature, and many of them claimed to be able to give rise toscale-invariant power spectrum as was favored by the observational data. It isthus interesting to think about whether there are some relations among them,e.g., the duality relation. In this paper, we investigate duality relationsbetween cosmological models in framework of general relativity (GR) , not onlywith varying slow-roll parameter $\epsilon$, but also with sound speed $c_s$,which can then be understood as "adiabatic duality". Several dualityrelationships are formulated analytically and verified numerically. We showthat models with varying $\epsilon$ and constant $c_s$ can be dual in scalarspectral index, but not tensor one. On the other hand, allowing both $\epsilon$and $c_s$ to vary can make models dual in both scalar and tensor spectralindices.

Adiabatic Duality: Duality of cosmological models with varying slow-roll parameter and sound speed