Dark Energy Parametrization motivated by Scalar Field Dynamics

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=\dotphi^2/2 and potential V.
• The equation of motion gives x=(L/6)(V/3H^2) and has a solution x=([(1+y)^2+2 L/3]^{1/2}-(1+y))/2 where y\equiv \rmm/V and L= (V'/V)^2 (1+q)^2, q=\ddotphi/V'.
• The resulting EoS is w=[6+ L- 6 \sqrt((1+y)^2+2L/3)]/(L+6y).