Title: Quantifying Scalar Field Dynamics with DESI 2024 Y1 BAO measurements

Abstract: Quintessence scalar fields are a natural candidate for evolving dark energy. Unlike the phenomenological $w_0w_a$ parameterization of the dark energy equation of state, they cannot accommodate the phantom regime of dark energy $w(z) < -1$, or crossings into the phantom regime. Recent baryon acoustic oscillation (BAO) measurements by the Dark Energy Spectroscopic Instrument (DESI) indicate a preference for evolving dark energy over a cosmological constant, ranging from $2.6\sigma-3.9\sigma$ when fitting to $w_0w_a$, and combining the DESI BAO measurements with other cosmological probes. In this work, we directly fit three simple scalar field models to the DESI BAO data, combined with cosmic microwave background anisotropy measurements and supernova data sets. Quantifying the preference for scalar field dynamics exhibited by the data, we find that $2-4\%$ of kinetic scalar field energy $\Omega_{\rm scf,k}$, is preferred over $\Lambda$CDM at the $95\%$ confidence level, for a canonical scalar field with a quadratic or linear potential. Fitting to the supernova data sets Pantheon, Pantheon+, DES-Y5, and Union3, we show that the mild tension ($n_{\sigma}< 3.4 $) under $\Lambda$CDM emerges from a BAO preference for smaller values of fractional mass-energy density $\Omega_m < 0.29$, while all supernova data sets, except for Pantheon, prefer larger values, $\Omega_m > 0.3$. The tension under $\Lambda$CDM remains noticeable ($n_{\sigma} <2.8$), when replacing two of the DESI BAO measurements redshift bins with effective redshifts $z_{\text{eff}} =0.51$, and $z_{\text{eff}}= 0.706$ with comparable BOSS DR 12 BAO measurements at $z_{\text{eff}} =0.51$, and $z_{\text{eff}}= 0.61$. Canonical scalar fields as dark energy are successful in mitigating that tension.