CMB Polarization can constrain cosmology better than CMB temperature

TL;DR

This study shows that for a cosmic variance limited CMB experiment, polarization—particularly the $EE$ power spectrum—can outperform temperature in constraining cosmological parameters, with $EE$ improving several parameters by up to a factor of $\sim2.8$ over $30\le \ell \le 2500$ and $TE$ offering comparable gains. Through Fisher forecast analysis for both a CVL and a Planck-like mission, the paper demonstrates that polarization provides stronger or comparable constraints to $TT$, largely due to sharper polarization peak features and enhanced degeneracy breaking via lensing and reionization signatures. The work further analyzes the dependence on $\ell_{\max}$ and $\ell_{\min}$, showing that low-$\ell$ polarization critically aids degeneracy breaking for $\Lambda$CDM parameters, while high-$\ell$ polarization contributes via lensing effects. For standard $\Lambda$CDM extensions, $EE$ excels for $\sum m_\nu$, whereas $TE$ more tightly constrains $N_{\rm eff}$, $Y_p$, and $n_{run}$, with Planck-like results favoring TT for extensions but still benefiting from polarization as a cross-check and robustness aid. Overall, the findings highlight the potential of polarization-focused CMB missions to yield cleaner, tighter cosmological constraints than temperature alone, influencing the design of future surveys such as CORE or PRISM.

Abstract

We demonstrate that for a cosmic variance limited experiment, CMB E polarization alone places stronger constraints on cosmological parameters than CMB temperature. For example, we show that EE can constrain parameters better than TT by up to a factor 2.8 when a multipole range of l=30-2500 is considered. We expose the physical effects at play behind this remarkable result and study how it depends on the multipole range included in the analysis. In most relevant cases, TE or EE surpass the TT based cosmological constraints. This result is important as the small scale astrophysical foregrounds are expected to have a much reduced impact on polarization, thus opening the possibility of building cleaner and more stringent constraints of the LCDM model. This is relevant specially for proposed future CMB satellite missions, such as CORE or PRISM, that are designed to be cosmic variance limited in polarization till very large multipoles. We perform the same analysis for a Planck-like experiment, and conclude that even in this case TE alone should determine the constraint on $Ω_ch^2$ better than TT by 15%, while determining $Ω_bh^2$, $n_s$ and $θ$ with comparable accuracy. Finally, we explore a few classical extensions of the LCDM model and show again that CMB polarization alone provides more stringent constraints than CMB temperature in case of a cosmic variance limited experiment.

Figures (16)

• Figure 1: Derivatives of the $C^{TT}_\ell$ (top panel), $C^{EE}_\ell$ (middle panel) and $C^{TE}_\ell$ (bottom panel) power spectrum with respect to the $\Lambda$CDM parameters. The plot is in logarithmic scale, so we plot the absolute value of the derivatives, showing negative values as dashed lines.
• Figure 2: Signal-to-noise for a Planck-like full mission experiment (solid lines) with $f_{\rm sky}=0.5$, as detailed in Table \ref{['tab:exp']}, for the $C^{TT}_\ell$ (blue), $C^{EE}_\ell$ (red) and $C^{TE}_\ell$ (green) power spectra. Dashed lines show the signal to noise for a CVL experiment with $f_{\rm sky}=1$.
• Figure 3: Standard deviations on $\Lambda CDM$ parameters as function of $\ell{\mathrm{max}}$ℓ_max$$, normalized to the standard deviation $\sigma^{\rm ref}$ obtained from $C^{TT}_\ell$ with $\ell{\mathrm{max}}$ℓ_max$=2500$. We consider a CVL experiment with $\ell{\mathrm{min}}$ℓ_min$=30$ and a prior on $\tau$. We consider here lensed CMB power spectra.
• Figure 4: Same as Fig. \ref{['lensedCVL']}, but for unlensed CMB power spectra.
• Figure 5: Same as Fig. \ref{['lensedCVL']}, but the constraints in this case are calculated as the inverse of the diagonal of the Fisher Matrix, i.e. they are not marginalized over degeneracies between parameters. By comparing with Fig. \ref{['lensedCVL']}, one can determine whether constraints on the parameters are limited by their degeneracies or by the sensitivity of the spectra to each parameter separately.