Impact of CMB low-$\ell$ EE polarization data on dark energy parameterizations

Title: Impact of CMB low-ℓ EE Polarization Data on Dark Energy Parameterizations

Problem Statement
The measurement of the optical depth to reionization ($\tau_{\text{reio}}$) is primarily driven by the large-scale E-mode polarization of the Cosmic Microwave Background (CMB) at multipoles $\ell < 30$. Recent analyses suggest that removing this low-ℓ EE data may alleviate various cosmological tensions, particularly those related to dynamical dark energy (DDE). While previous studies have noted that the tension between low-intermediate redshift Baryon Acoustic Oscillation (BAO) data and high-redshift CMB data could be explained by unknown systematics in large-scale polarization measurements, the extent to which $\tau_{\text{reio}}$ sensitivity persists across different Dark Energy (DE) parameterizations remains to be fully explored. This work investigates the impact of excluding low-ℓ EE data on the constraints of the Chevallier-Polarski-Linder (CPL), Jassal-Bagla-Padmanabhan (JBP), and Barboza-Alcaniz (BA) DE parameterizations, comparing them against the standard $\Lambda$CDM model.

Methodology
The authors constrain the DE parameterizations using a combination of CMB data from the Planck satellite and the Atacama Cosmology Telescope Data Release 6 (ACT DR6), supplemented by DESI BAO measurements (DR2) and the PantheonPlus compilation of Type Ia Supernovae (SNe Ia).

Two distinct data combinations are analyzed:

1. Full Dataset: CMB + SNe + BAO, including low-ℓ EE polarization likelihoods (provided by the sroll2 likelihood for Planck and ACT).
2. Excluded Dataset: CMB + SNe + BAO, with the low-ℓ EE likelihood removed. In this scenario, $\tau_{\text{reio}}$ is constrained primarily through parameter degeneracies, specifically the $A_s - \tau_{\text{reio}}$ degeneracy, rather than direct polarization constraints.

The analysis utilizes the Boltzmann code CLASS for linear theory predictions and hmcode for non-linear corrections. Bayesian inference is performed using Cobaya, with Markov Chain Monte Carlo (MCMC) chains analyzed via GetDist. Model performance is evaluated using the Akaike Information Criterion (AIC) and the Deviance Information Criterion (DIC) relative to the $\Lambda$CDM reference model.

Key Results

• Shifts in $\tau_{\text{reio}}$ and $A_s$: Excluding low-ℓ EE data shifts the central values of $\tau_{\text{reio}}$ and the primordial power spectrum amplitude ($A_s$) to higher values. This is driven by the unbroken $A_s - \tau_{\text{reio}}$ degeneracy.

  • For $\Lambda$CDM and JBP, $A_s$ shifts upward by $\sim(1.4 - 1.8)\sigma$.
  • For CPL and BA, the shift is milder, at $\sim 1\sigma$.
  • The error bars on $A_s$ relax significantly (by $\sim 50-120\%$) when low-ℓ EE data is excluded, with the relaxation being more pronounced for CPL and BA.

• Equation of State (EOS) Evolution: The exclusion of low-ℓ EE data drives the EOS parameters ($w_0, w_a$) for all three parameterizations toward the quintessence regime ($w(z) > -1$).

  • This shift is primarily driven by the strengthening of the $w_a - A_s$ and $w_a - \tau_{\text{reio}}$ correlations.
  • The effect is most prominent in the JBP parameterization, where the EOS lies entirely within the quintessence regime at the $1\sigma$ confidence level when low-ℓ EE data is excluded.

• Parameter Correlations:

  • In $\Lambda$CDM, excluding low-ℓ EE data strengthens the $A_s - \tau_{\text{reio}}$ correlation, which propagates to $\sigma_8$, causing a $\sim 1.5\sigma$ upward shift in $\sigma_8$.
  • In DE parameterizations, the $A_s - \sigma_8$ and $\sigma_8 - \tau_{\text{reio}}$ correlations remain relatively weak or moderate. The additional freedom provided by $w_0$ and $w_a$ absorbs the upward pull on $\sigma_8$, resulting in no significant shift in the central $\sigma_8$ values, though error bars do widen slightly.
  • A strong negative correlation between $w_0$ and $w_a$ leads to partial cancellations in the net EOS response to the $\tau_{\text{reio}}$ shift, explaining the relatively small shifts in $w(z)$ compared to the shifts in $A_s$.

• Model Comparison:

  • AIC: Shows positive evidence in favor of CPL and BA over $\Lambda$CDM, and weak evidence for JBP. These results are robust to the inclusion or exclusion of low-ℓ EE data.
  • DIC: Shows mild sensitivity to the dataset used.
    • For both Planck and ACT DR6, CPL and BA show positive evidence over $\Lambda$CDM when excluding low-ℓ EE data, changing to strong evidence when including it.
    • For JBP, ACT DR6 yields weak positive evidence over $\Lambda$CDM regardless of low-ℓ EE inclusion. However, Planck data weakly favors $\Lambda$CDM over JBP regardless of low-ℓ EE inclusion.
  • Drivers of Improvement: The improvement in fit ($\Delta \chi^2$) for DE models is primarily driven by the SNe likelihood, with non-negligible contributions from high-ℓ TT/TE/EE CMB data for CPL and BA. BAO contributes a consistent $\Delta \chi^2 \sim -2$. Low-ℓ EE and lensing contributions are negligible.

Significance and Conclusions
The paper concludes that $\tau_{\text{reio}}$ acts as a common thread underlying multiple current cosmological tensions, including the apparent preference for dynamical dark energy and the unphysical preference for negative neutrino masses found in some analyses. The findings suggest that the evidence for evolving dark energy is sensitive to the treatment of large-scale polarization data.

The authors emphasize that the constraints on $\tau_{\text{reio}}$ are currently dependent on a single dataset (large-scale CMB polarization). The results highlight the necessity of constraining $\tau_{\text{reio}}$ more efficiently using independent methods to avoid biases in cosmological parameter estimation. The study also notes that recent updates to the DES SNe sample (DES-Dovekie) reduce the evidence for DDE, suggesting that the specific SNe sample used significantly influences the final conclusions, a factor the authors acknowledge in their analysis.