Can cosmological observations uniquely determine the nature of dark energy ?

TL;DR

This paper demonstrates that the two key parameters, equation of state and effective speed of sound, do not uniquely determine the scalar field Lagrangian of dark energy, as different models can produce identical observational signatures.

Contribution

It shows that scalar field dark energy models cannot be uniquely identified by these parameters alone, even with perturbation data.

Findings

Different scalar field Lagrangians can produce identical $w$ and $c_e^2$ values.

Background and perturbation evolutions are indistinguishable for certain dark energy models.

Parameters $w$ and $c_e^2$ are insufficient to uniquely determine the dark energy Lagrangian.

Abstract

The observational effect of all minimally coupled scalar field models of dark energy can be determined by the behavior of the following two parameters : (1) equation of state parameter $w$, which relates dark energy pressure to its energy density, and (2) effective speed of sound $c_{e}^{2}$, which relates dark energy pressure fluctuation to its density fluctuation. In this paper we show that these two parameters do not uniquely determine the form of a scalar field dark energy Lagrangian even after taking into account the perturbation in the scalar field. We present this result by showing that two different forms of scalar field Lagrangian can lead to the same values for these paired parameters. It is well known that from the background evolution the Lagrangian of the scalar field dark energy cannot be uniquely determined. The two models of dark energy presented in this paper are indistinguishable from the evolution of background as well as from the evolution of perturbations from a FRW metric.