Can cosmological observations uniquely determine the nature of dark energy ?

Understand

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.