Eliminating the optical depth nuisance from the CMB with 21 cm cosmology

TL;DR

This paper tackles the problem that the CMB optical depth $τ$ degrades constraints on other cosmological parameters. It proposes two complementary 21 cm approaches to predict or constrain $τ$: (i) a power-spectrum method using semi-analytic reionization models to derive $τ$, and (ii) a global 21 cm signal method to constrain low-redshift $τ$ in a more model-independent way. Through Fisher-matrix forecasts for HERA and Planck priors, the authors show substantial improvements in $A_s$ and neutrino-mass constraints, driven by breaking the $A_s$–$τ$ degeneracy, and they discuss model-dependence and the role of global-signal measurements as robust cross-checks. The results demonstrate that 21 cm cosmology can both illuminate reionization astrophysics and significantly enhance broader cosmological inferences, including potential precision measurements of the sum of neutrino masses.

Abstract

Amongst standard model parameters that are constrained by cosmic microwave background (CMB) observations, the optical depth $τ$ stands out as a nuisance parameter. While $τ$ provides some crude limits on reionization, it also degrades constraints on other cosmological parameters. Here we explore how 21 cm cosmology---as a direct probe of reionization---can be used to independently predict $τ$ in an effort to improve CMB parameter constraints. We develop two complementary schemes for doing so. The first uses 21 cm power spectrum observations in conjunction with semi-analytic simulations to predict $τ$. The other uses global 21 cm measurements to directly constrain low redshift (post-reheating) contributions to $τ$ in a relatively model-independent way. Forecasting the performance of the upcoming Hydrogen Epoch of Reionization Array, we find that significant reductions in the errors on $τ$ can be achieved. These results are particularly effective at breaking the CMB degeneracy between $τ$ and the amplitude of the primordial fluctuation spectrum $A_s$, with errors on $\ln (10^{10} A_s)$ reduced by up to a factor of four. Stage 4 CMB constraints on the neutrino mass sum are also improved, with errors potentially reduced to $12\,\textrm{meV}$ regardless of whether CMB experiments can precisely measure the reionization bump in polarization power spectra. Observations of the 21 cm line are therefore capable of improving not only our understanding of reionization astrophysics, but also of cosmology in general.

Figures (11)

• Figure 1: Fractional error in $\tau$ induced by uncertainties in helium reionization as a function of the redshift of helium reionization $z_\textrm{ion,He}$ and the uncertainty in this redshift $\delta z_\textrm{ion,He}$. For reasonable values of these parameters, the errors arising from uncertainties in helium reionization are subdominant to those arising from cosmological parameter uncertainty. It is thus permissible to neglect uncertainties in helium reionization.
• Figure 2: Cumulative contribution to the optical depth $\tau$ from low to high redshift, for several different models of reionization. The crucial astrophysical quantity for a precise determination of $\tau$ is the density-weighted ionized fraction. This depends on the correlation between the ionization field and the density field. The different reionization models shown here reflect different models for this correlation, which must be known for a precise prediction of $\tau$, given the spread seen here.
• Figure 3: Top row: Simulation of the nonlinear density field over the past light cone that is observed by a $21\,\textrm{cm}$ experiment. Second row: Corresponding ionization fraction, assuming $(T_\textrm{vir}, R_\textrm{mfp}, \zeta) = (6 \times 10^4\,\textrm{K}, 35\,\textrm{Mpc}, 30)$ to match the optical depth of Planck TT,TE,EE + lowP + lensing + ext. Third row: Corresponding ionized fraction history $\overline{x}_\textrm{HII}$ (red solid curve) and the density-weighted ionization history $\overline{x_\textrm{HII} (1+ \delta_b)}$ (black solid curve). The averaged ionized fraction is also seen to be a poor approximation for the density-weighted ionized fraction, which is the crucial quantity for determining $\tau$. Bottom row: Corresponding $21\,\textrm{cm}$ power spectra (black) at various redshifts, plotted as $\Delta^2_{21} (k) \equiv k^3 P_{21}(k) / 2 \pi^2$. Blue and orange curves show power spectra for different values of $T_\textrm{vir}$. Note that this figure is intended for illustrative purposes only, and that the scales on the top two rows do not correspond exactly to the redshift axis on the third row. In our proposed analysis, one measures the bottom row through observations, constraining underlying model parameters that are then fed into simulations to produce the top two rows. The density-weighted ionization fraction (third row) is then extracted and inserted into Eq. \ref{['eq:tauH']} to determine $\tau$.
• Figure 4: Forecasted $68\%$ and $95\%$ confidence regions (black ellipses) in the $T_\textrm{vir}$-$\zeta$ parameter space for HERA observations, along with 21cmFAST-predicted optical depth $\tau$ (filled color contours). The rough alignment of the degeneracy directions suggest that uncertainties in astrophysical parameters arising from $21\,\textrm{cm}$ power spectrum measurements are unlikely to seriously compromise one's ability to make highly precise predictions of $\tau$.
• Figure 5: Likelihood contours for $\Lambda$CDM cosmological parameters as defined in the publicly released Planck TT,TE,EE + lowP + lensing + ext dataset. Black ellipses show $68\%$ and $95\%$ confidence regions for every parameter against $\tau$. Red lines indicate values of $\tau$ as predicted in 21cmFAST and approximated by Eq. \ref{['eq:TTTEEE_linearTau']}, holding all other parameters fixed. The blue dashed line in the $\tau$-$\ln(10^{10}A_s)$ plot indicates constant $A_s e^{-2\tau}$, illustrating the strong degeneracy inherent in CMB observations that we expect to be broken by $21\,\textrm{cm}$ observations.