Cosmological constraints on nonphantom dynamical dark energy with DESI Data Release 2 Baryon Acoustic Oscillations: A 3$σ$+ lensing anomaly

TL;DR

This work tests a non-phantom dynamical dark energy (NPDDE) model with $12$ parameters, enforcing $w(z) \ge -1$ to realize quintessence-like behavior, and analyzes DESI DR2 BAO, Planck PR4 CMB and lensing, Pantheon+ and DESY5 SN, and DES Y1 weak lensing. Using Cobaya/CAM B, the authors find a robust lensing anomaly with $A_{\rm lens} > 1$ at >3$\sigma$ significance when WL data are included, and $>2$$\sigma$ without WL, implying more CMB lensing than predicted by NPDDE; this anomaly correlates with $S_8$ and with the DE equation of state, complicating the interpretation of quintessence models. Neutrino mass bounds are tightened by the non-phantom constraint but are weakened by the $A_{\rm lens}$–$\sum m_ν$ degeneracy; $N_{\rm eff}$ is mildly above the standard value, and the Hubble tension persists at about 3–4$\sigma$. The results underscore that realistic quintessence-like cosmologies must contend with the lensing anomaly, potentially pointing to new physics or unresolved systematics, and highlight the need for future high-precision CMB and large-scale structure data to clarify the origin of the anomaly.

Abstract

We consider a 12-parameter cosmological model with non-phantom dynamical dark energy (NPDDE), where non-phantom implies that the equation of state (EoS) of dark energy (DE), $w(z)\geq-1$ for all redshifts $z$. Thus, the DE EoS covers the parameter space corresponding to the popular single scalar-field dark energy models, i.e., Quintessence. The cosmological model comprises 6 parameters of the $Λ$-Cold Dark Matter ($Λ$CDM) model, and additionally the dynamical DE EoS parameters ($w_0$, $w_a$), the scaling of the lensing amplitude ($A_{\rm lens}$), sum of the neutrino masses ($\sum m_ν$), the effective number of non-photon relativistic degrees of freedom ($N_{\rm eff}$), and the running of the scalar spectral index ($α_s$). We derive constraints on the parameters by combining the latest Dark Energy Spectroscopic Instrument (DESI) Data Release (DR) 2 Baryon Acoustic Oscillation (BAO) measurements with cosmic microwave background (CMB) power spectra from Planck Public Release (PR) 4, CMB lensing data from Planck PR4 and Atacama Cosmology Telescope (ACT) DR6, uncalibrated Type Ia supernovae (SNe) data from the Pantheon+ and Dark Energy Survey (DES) Year 5 (DESY5) samples, and Weak Lensing (WL) data from DES Year 1. Our major finding is that with CMB+BAO+WL and CMB+BAO+SNe+WL, we find 3$σ$+ evidence for $A_{\rm lens} >1$, indicating a higher than expected CMB lensing amplitude relative to the NPDDE prediction of unity. This implies that for cosmology to accommodate realistic quintessence-like dark energy models (as opposed to unrealistic phantom DE), one would also need to explain a relatively significant presence of the lensing anomaly.

Figures (4)

• Figure 1: The CMB lensing-potential powerspectrum for different values of the constant DE EoS $w$. The angular scale of sound horizon at recombination, $\theta_s^*$, is kept fixed by adjusting $H_0$.
• Figure 2: 68% and 95% marginalised contours in the $w_{0,\rm DE} - w_{a,\rm DE}$ plane for different data combinations. The area to the right of the vertical dashed blue line and above the slanted dashed blue line represents the parameter space corresponding to quintessence-like or non-phantom dark energy.
• Figure 3: The left panel shows the 1D posterior distributions of $A_{\rm lens}$ for various data combinations. The right panel shows its 2D correlation plots with the $S_8$ parameter. We note that dataset combinations with WL included leads to a 3$\sigma$+ lensing anomaly due to the strong negative correlation with $S_8$. Even without the WL data, the lensing anomaly is 2$\sigma$+.
• Figure 4: The left, middle, and right panels show the 1D posterior distributions of $\sum m_{\nu}$, $N_{\rm eff}$, and $H_0$ (km/s/Mpc) respectively, for various data combinations. The dashed vertical line in the middle panel corresponds to the standard model value of $N_{\rm eff} = 3.044$.