Dark Energy Parametrization motivated by Scalar Field Dynamics
  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). Since the universe is accelerating
at present time we use the slow roll approximation in which case we have |q|<<
1 and L\simeq (V'/V)^2. However, the derivation of w is exact and has no
approximation. By choosing an appropriate ansatz for L we obtain a wide class
of behavior for the evolution of Dark Energy without the need to specify the
potential V. The EoS w can either grow and later decrease, or other way around,
as a function of redshift and it is constraint between -1\leq w\leq 1 as for
any canonical scalar field with only gravitational interaction. To determine
the dynamics of Dark Energy we calculate the background evolution and its
perturbations, since they are important to discriminate between different DE
models. Our parametrization follows closely the dynamics of a scalar field
scalar fields and the function L allow us to connect it with the potential
V(phi) of the scalar field phi.
