Quantifying Scalar Field Dynamics with DESI 2024 Y1 BAO measurements

TL;DR

The paper benchmarks three physically motivated dark-energy models against DESI Y1 BAO data in combination with CMB and SN datasets, focusing on thawing canonical scalar fields with quadratic or linear potentials (SCF QUAD and SCF LIN) and a dark-energy-radiation scenario (SCF DER). By fitting to $D_M/r_d$ and $D_H/r_d$ measurements and SN luminosity distances, the authors quantify the present-day kinetic energy fraction $\Omega_{\rm scf,k}$ or dark-energy-radiation fraction $\Omega_{\rm der}$ and map these to $w(z)$, comparing to the phenomenological $w_0w_a$ parameterization. They find modest evidence for evolving dark energy: $\Omega_{\rm scf,k}$ at the few-percent level (2–4%) for SCF QUAD/LIN and $\Omega_{\rm der}$ at 1–4% for SCF DER, with DES-Y5 and Union3 SN data driving the signal; yet $\Lambda$CDM remains within 95% CL for all dataset combinations. Importantly, these scalar-field models alleviate the tension between SN and BAO data under $\Lambda$CDM and reduce non-Gaussian tension between SN and CMB+DESI, while preserving neutrino mass constraints close to the standard model, suggesting canonical scalar fields as viable explanations for DESI BAO hints without phantom crossing.

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 $2.6σ-3.9σ$ 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. We find the best fit model to include a $2-4\%$ kinetic scalar field energy $Ω_{\rm scf,k}$, for a canonical scalar field with a quadratic or linear potential. However, only the DESY-Y5 supernova data set combination shows a preference for quintessence over $Λ$CDM at the $95\%$ confidence level. Fitting to the supernova data sets Pantheon, Pantheon+, DES-Y5, and Union3, we show that the mild tension ($n_σ< 3.4 $) under $Λ$CDM emerges from a BAO preference for smaller values of fractional mass-energy density $Ω_m < 0.29$, while all supernova data sets, except for Pantheon, prefer larger values, $Ω_m > 0.3$. The tension under $Λ$CDM remains noticeable ($n_σ <2.8$), when replacing two of the DESI BAO 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.

Figures (12)

• Figure 1: Comparison of the dark energy equation of state $w(z)$ as a function of redshift for the three scalar field cosmologies described in Sec. \ref{['sec:models']} for the same value $w(0)=-0.914$, as well as the phenomenological $w_0w_a$ thawing parameterization, described in Appendix \ref{['sec:w0wa']}, that mimics thawing scalar field dynamics. The curves correspond to values of $\Omega_{\text{scf,k}} = 0.03$, $\Omega_{\text{der}} = 0.09$, and $w_{\text{thawing}} = -0.914$, for fixed $\Omega_m= 0.3$ for all curves. The dashed vertical lines indicate the effective redshifts $z_{\text{eff}}$ of the DESI BAO measurements.
• Figure 2: (Top Panels) Supernova and BAO $\chi^2$-posteriors for $\Lambda$CDM in combination with CMB Planck and various supernova data sets. Two BAO data set combinations are shown, DESI to the left, and DESI$^{\star}$+BOSS$^{\star}_{\rm DR12}$, where we have replaced the DESI BAO $z_{\text{eff}} =0.51$, and $z_{\text{eff}} =0.706$ data points with comparable redshift BOSS DR12 measurements. The CMB Planck data has a reduced $\ell < 1296$ range to avoid nonlinear lensing effects. The opposing preference for $\Omega_m$ in $\chi^2_{\text{SN}}$ and $\chi^2_{\text{BAO}}$ indicates a mild tension of the datasets under $\Lambda$CDM. The shown supernova $\chi^2_{\text{SN}}$ for Pantheon, Pantheon+, DES-Y5, and Union3 have, respectively, the constant offset $\chi^2_{\rm SN, offset} = (1034.8, 1405.7, 1648.4, 31.5)$. (Bottom Panels) Probability distribution of the difference $\Delta \Omega_m$ between $\Omega_m$ density derived from CMB + BAO versus SN-only MCMC chains. Replacing DESI bins at $z_{\text{eff}} =0.51$, and $z_{\text{eff}} =0.706$ with BOSS DR12 measurement does not significantly reduces the tension on $\Omega_m$ values between CMB+BAO and newer Type-Ia supernova measurements that drive the detection of dynamical dark energy. Appendix \ref{['sec:w0wa']} shows that the CMB+DESI combination is perfectly compatible with the cosmological constant as long as type-Ia supernova constrains the cold dark matter density to be $\Omega_m \approx 0.289$, which is the range preferred by the Pantheon data set.
• Figure 3: Marginalized posteriors for a scalar field with a quadratic potential (SCF QUAD) to the left and a linear potential (SCF LIN) to the right. The supernova $\chi^2_{\text{SN}}$ are shown with the same offset as before. The models allow a better fit to supernova data for smaller $\Omega_m$, easing the tension under $\Lambda$CDM shown in Fig. \ref{['fig:LCDM']}.
• Figure 4: Marginalized posteriors for dark energy radiation (SCF DER), where the dynamical component is dark radiation rather than kinetic energy. The supernova $\chi^2_{\text{SN}}$ is shown with a constant offset. The model's ability to improve the fit to supernova data for smaller values of $\Omega_m$ is worse than SCF QUAD, and SCF LIN. The $95\%$ confidence interval includes $\Lambda$CDM ($\Omega_{\text{der}} = 0$) for all of the dataset combinations explored in this work.
• Figure 5: Comparison of the various $\chi^2_{\text{SN}}$ (top panel), and DESI BAO $\chi^2_{\text{BAO}}$ (bottom panel) values, between $\Lambda$CDM, $w_0w_a$, and our three scalar field cosmologies. Evolving dark energy cosmologies improve the fit to supernova significantly for Pantheon+, DES-Y5, and Union3. While the peaks of the evolving dark energy models $\chi^2_{\rm{SN}}$ for Pantheon are larger than the $\Lambda$CDM value, the tails of the distributions can achieve a better fit than $\Lambda$CDM. For $\chi^2_{\rm{BAO}}$, the evolving scalar field models perform comparably to $\Lambda$CDM, while the $w_0w_a$ model achieves a slightly lower $\chi^2_{\rm{BAO}}$ value. The supernova $\chi^2_{\text{SN}}$ are shown with the same offset as before.