A note on the equivalence of a barotropic perfect fluid with a K-essence scalar field

Understand

In this short note, we obtain the necessary and sufficient condition for a class of non-canonical single scalar field models to be exactly equivalent to barotropic perfect fluids, under the assumption of an irrotational fluid flow.

• An immediate consequence of this result is that the non-adiabatic pressure perturbation in this class of scalar field systems vanishes exactly at all orders in perturbation theory and on all scales.
• The Lagrangian for this general class of scalar field models depends on both the kinetic term and the value of the field.
• However, after a field redefinition, it can be effectively cast in the form of a purely kinetic K-essence model.