Scalar field dark energy models: Current and forecast constraints

Recent results from Type Ia supernovae (SNe Ia) and baryon acoustic oscillations (BAO), in combination with cosmic microwave background (CMB) measurements, have focused renewed attention on dark energy models with a time-varying equation-of-state parameter, $w(z)$. In this paper, we describe the simplest, physically motivated models of evolving dark energy that are consistent with the recent data, a broad subclass of the so-called thawing scalar field models that we dub $w_\phi$CDM. We provide a quasi-universal, quasi-one-parameter functional fit to the scalar-field $w_\phi(z)$ that captures the behavior of these models more informatively than the standard $w_0w_a$ phenomenological parametrization; their behavior is completely described by the current value of the equation-of-state parameter, $w_0=w(z=0)$. Combining current data from BAO (DESI Data Release 2), the CMB (Planck and ACT), large-scale structure (DES Year-3 $3\times2$pt), SNe Ia (DES-SN5YR), and strong lensing (TDCOSMO + SLACS), for $w_\phi$CDM we obtain $w_0=-0.904_{-0.033}^{+0.034}$, 2.9$\sigma$ discrepant from the $\Lambda$ cold dark matter ($\Lambda$CDM) model. The Bayesian evidence ratio substantially favors this $w_\phi$CDM model over $\Lambda$CDM. The data combination that yields the strongest discrepancy with $\Lambda$CDM is BAO+SNe Ia, for which $w_0=-0.837^{+0.044}_{-0.045}$, $3.6\sigma$ discrepant from $\Lambda$CDM and with a Bayesian evidence ratio strongly in favor. We find that the so-called $S_8$ tension between the CMB and large-scale structure is slightly reduced in these models, while the Hubble tension is slightly increased. We forecast constraints on these models from near-future surveys (DESI-extension and the Vera C. Rubin Observatory LSST), showing that the current best-fit $w_\phi$CDM model will be distinguishable from $\Lambda$CDM at over 9$\sigma$.