  There have been thousands of cosmological models for our early universe
proposed in the literature, and many of them claimed to be able to give rise to
scale-invariant power spectrum as was favored by the observational data. It is
thus interesting to think about whether there are some relations among them,
e.g., the duality relation. In this paper, we investigate duality relations
between cosmological models in framework of general relativity (GR) , not only
with varying slow-roll parameter $\epsilon$, but also with sound speed $c_s$,
which can then be understood as "adiabatic duality". Several duality
relationships are formulated analytically and verified numerically. We show
that models with varying $\epsilon$ and constant $c_s$ can be dual in scalar
spectral 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 spectral
indices.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory