Scalar Field Dark Energy Parametrization

Understand

We propose a new Dark Energy parametrization based on the dynamics of a scalar field.

• We use an equation of state $w=(x-1)/(x+1)$, with $x=E_k/V$, the ratio of kinetic energy $E_k=\dot\phi^2/2$ and potential $V$.
• The eq.
• of motion gives $x=(L/6)(V/3H^2)$ and with a solution $x=([1+2 L/3(1+y)]^{1/2}-1)(1+y)/2$ where $y\equiv \rm/V$ and $L\equiv (V'/V)^2 (1+q)^2,\, q\equiv\ddot\p/V'$.