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

TL;DR

This paper explores the duality relations among various cosmological models with varying slow-roll parameters and sound speed, revealing conditions under which models are equivalent in their spectral indices.

Contribution

It introduces the concept of adiabatic duality in cosmological models with variable slow-roll parameters and sound speed, providing analytical formulations and numerical verifications.

Findings

Models with varying $psilon$ and constant $c_s$ are dual in scalar spectral index.

Allowing both $psilon$ and $c_s$ to vary can make models dual in both spectral indices.

Duality relations are formulated analytically and verified numerically.

Abstract

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.