Three fluid cosmological model using Lie and Noether symmetries

Understand

We employ a three fluid model in order to construct a cosmological model in the Friedmann Robertson Walker flat spacetime, which contains three types of matter dark energy, dark matter and a perfect fluid with a linear equation of state.

• Dark matter is described by dust and dark energy with a scalar field with potential V({\phi}).
• In order to fix the scalar field potential we demand Lie symmetry invariance of the field equations, which is a model-independent assumption.
• The requirement of an extra Lie symmetry selects the exponential scalar field potential.