Dynamical dark energy in light of DESI data and the null energy condition

Quintessence scalar fields are candidates for evolving dark energy. The Dark Energy Spectroscopic Instrument (DESI) collaboration recently released the first data results from the Baryonic Acoustic Oscillation (BAO) in the galaxy, quasar, and Lyman-α forest tracers, claiming a preference for evolving dark energy models when using Chevallier-Polarski-Linder (CPL) parameterization where w(z) = w₀ + w_a z / (1 + z). These observations favor a sector of the w₀ -w_a plane in which w₀ > −1 and w₀ + w_a < −1, suggesting that the null energy condition (NEC) is violated, but DESI does not quantify the strength of the tension with no NEC violation. In this work, I will perform the quantification for different quintessence models that satisfy the NEC limit. I will also look at the behavior of these models in the w₀ -w_a plane.