Cosmological constraints on the roll parameter of freezing and thawing quintessence models

We constrain the roll parameter of freezing and thawing quintessence scalar field models using cosmological observations that measure the expansion history of the Universe, by means of a dynamical system approach. The roll parameter is directly defined as λ≡ V′/(κV), and is directly related to the slope of the potential. Using the combined data sets of cosmological observations, we find the present-day values for the roll parameter to be λ = 0.0015±0.0005 and λ = 0.0014±0.0005 for the freezing and thawing cases, respectively, indicating a very slow-rolling potential, but still suggesting a difference with respect to the ΛCDM model. With a value of λ ≈ 10−3, we obtain a dark energy equation of state of wφ ≈ −0.9999 for both models.