Dispu$τ$able: the high cost of a low optical depth

TL;DR

The paper investigates how the optical depth to reionization, $τ$, influences tensions between DESI BAO and CMB within ΛCDM, focusing on neutrino mass and evolving dark energy. By examining priors on $τ$ and inferring $τ$ without low-ℓ CMB polarization, the authors show that larger $τ$ can move the inferred neutrino mass toward the minimal value and reduce the preference for dynamical dark energy, though the results welcome a tension with Planck’s low-ℓ polarization measurements. Using DESI+CMB+lensing+BAO data without low-ℓ polarization yields $τ≈0.090–0.095$, suggesting a potential “$τ$ tension” within ΛCDM that motivates future large-scale CMB and reionization probes. Overall, $τ$ emerges as a crucial parameter that strongly affects key cosmological inferences and may reconcile some current discrepancies if future measurements support higher values.

Abstract

Recent Baryonic Acoustic Oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) are mildly discrepant ($2.2σ$) with the Cosmic Microwave Background (CMB) when interpreted within $Λ$CDM. When analyzing these data with extended cosmologies this inconsistency manifests as a $\simeq3σ$ preference for sub-minimal neutrino mass or evolving dark energy. It is known that the preference for sub-minimal neutrino mass from the suppression of structure growth could be alleviated by increasing the optical depth to reionization $τ$. We show that, because the CMB-inferred $τ$ is negatively correlated with the matter fraction, a larger optical depth resolves a similar preference from geometric constraints. Optical depths large enough to resolve the neutrino mass tension ($τ\sim0.09)$ also reduce the preference for evolving dark energy from $\simeq3σ$ to $\simeq1.5σ$. Conversely, within $Λ$CDM the combination of DESI BAO, high-$\ell$ CMB and CMB lensing yields $τ= 0.090 \pm 0.012$. The required increase in $τ$ is in $\simeq3-5σ$ tension with Planck low-$\ell$ polarization data when taken at face value. While there is no evidence for systematics in the large-scale Planck data, $τ$ remains the least well-constrained $Λ$CDM parameter and is far from its cosmic variance limit. The importance of $τ$ for several cosmological measurements strengthens the case for future large-scale CMB experiments as well as direct probes of the epoch of reionization.

Figures (4)

• Figure 1: Left: Constraints on $\tau$ and $\Omega_{\rm m}$ from the joint analysis of high-$\ell$ CMB and CMB lensing. The dashed yellow line $(\Omega_{\rm m}(\tau)=0.349-0.505\,\tau)$ approximates the $\tau-\Omega_{\rm m}$ degeneracy direction. Right:$\Lambda$CDM constraints from BAO (blue) or CMB high-$\ell$ primary and lensing with a $\tau$ prior (pink/black).
• Figure 2: Constraints on $M_{\nu,\mathrm{eff}}$ from the joint analysis of BAO and CMB data when including a $\tau$ prior ($\tau=0.06$ in pink and $\tau=0.09$ in black) or low-$\ell$ data from Planck (orange).
• Figure 3: Constraints on the $w_0w_a$ model from the combination of high-$\ell$ primary CMB data, CMB lensing, DESI BAO and a prior on the optical depth. Locations of posterior maxima are indicated by triangles.
• Figure 4: When discarding the low-$\ell$ data from Planck we infer $\tau=0.090\pm 0.012$ within $\Lambda$CDM from the combination of high-$\ell$ CMB, CMB lensing and BAO, or $\tau=0.095\pm 0.014$ for $\Lambda{\rm CDM}+\sum m_\nu$ with a physical prior of $\sum m_\nu \geq 0.06$ eV.