How accurately can 21 cm tomography constrain cosmology?

There is growing interest in using 3-dimensional neutral hydrogen mapping with the redshifted 21 cm line as a cosmological probe. However, its utility depends on many assumptions. To aid experimental planning and design, we quantify how the precision with which cosmological parameters can be measured depends on a broad range of assumptions, focusing on the 21 cm signal from $6<z<20$. We cover assumptions related to modeling of the ionization power spectrum, to the experimental specifications like array layout and detector noise, to uncertainties in the reionization history, and to the level of contamination from astrophysical foregrounds. We derive simple analytic estimates for how various assumptions affect an experiment’s sensitivity, and we find that the modeling of reionization is the most important, followed by the array layout. We present an accurate yet robust method for measuring cosmological parameters that exploits the fact that the ionization power spectra are rather smooth functions that can be accurately fit by 7 phenomenological parameters. We find that for future experiments, marginalizing over these nuisance parameters may provide constraints almost as tight on the cosmology as if 21 cm tomography measured the matter power spectrum directly. A future square kilometer array optimized for 21 cm tomography could improve the sensitivity to spatial curvature and neutrino masses by up to 2 orders of magnitude, to $\Delta {\Omega }_k\approx 0.0002$ and $\Delta m_{\nu }\approx 0.007\mathrm{eV}$, and give a $4\sigma$ detection of the spectral index running predicted by the simplest inflation models.

Figure 1

The 21 cm tomography can potentially map most of our observable Universe (light blue/light gray), whereas the CMB probes mainly a thin shell at $z\sim {10}^3$ and current large-scale structure surveys (here exemplified by the Sloan Digital Sky Survey and its luminous red galaxies) map only small volumes near the center. This paper focuses on the convenient $7\lesssim z\lesssim 9$ region (dark blue/dark gray).

Figure 2

Fits to the ionization power spectra at several redshifts. Solid (blue) lines are the results of the radiative transfer simulation in model I of the McQuinn et al. paper [30]. Dashed (green) lines are fitting curves of our parametrization. Dot-dashed (red) lines are best fits using the parametrization suggested by Santos and Cooray [3]. Top panels: ${\mathcal{P}}_{xx}/{\mathcal{P}}_{\delta \delta }=P_{\mathrm{xx}}/({\overline{x}}_{\mathrm{H}}^2{P}_{\delta \delta })$. Bottom panels: ${\mathcal{P}}_{x\delta }/{\mathcal{P}}_{\delta \delta }=P_{\mathrm{x}\delta }/({\overline{x}}_{\mathrm{H}}{P}_{\delta \delta })$. From left to right: $z=9.2$, 8.0, 7.5, 7.0 (${\overline{x}}_{\mathrm{i}}=0.10$, 0.30, 0.50, 0.70, respectively).

Figure 3

Examples of array configuration changes. For MWA (upper panels), antennae are uniformly distributed inside the nucleus radius $R_0$, and the density $\rho$ falls off like a power law for $R_0<r<R_{\mathrm{in}}$, where $R_{\mathrm{in}}$ is the core radius. For SKA (lower panels) and similarly for LOFAR, there is, in addition, a uniform yet dilute distribution of antennae in the annulus $R_{\mathrm{in}}<r<R_{\mathrm{out}}$, where $R_{\mathrm{out}}$ is the outer annulus radius. When $R_0$ is decreased ($R_0=0.7/0.5/0.3\times R_0^{\max }$) with $R_{\mathrm{in}}=3.0\times R_0^{\max }$ fixed (left panels), the density in the core falls off more slowly (blue/red/green curves). When $R_{\mathrm{in}}$ is decreased ($R_{\mathrm{in}}=4.0/3.0/2.0\times R_0^{\max }$) with $R_0=0.5\times R_0^{\max }$ fixed (right panels), the density in the core also falls off less steeply (dashed/solid/dotted curves).

Figure 4

Available $(k_{\perp },k_{\parallel })$ pixels from MWA (upper left), FFTT (upper right), LOFAR (lower left), and SKA (lower right), evaluated at $z=8$. The blue/ gray regions can be measured with good signal-to-noise ratios from the nucleus and core of an array, while the cyan/light- gray regions are measured only with the annulus and have so poor signal-to-noise ratios that they hardly contribute to cosmological parameter constraints.

Figure 5

Relative $1\sigma$ error for measuring ${\mathcal{P}}_{\delta \delta }(k)$ with the PESS model by observing a 6 MHz band that is centered at $z=8$ with MWA (red/solid line), LOFAR (blue/short-dashed line), SKA (green/dotted line), and FFTT (cyan/long-dashed line). The step size is $\Delta \ln k\approx 0.10$.

Figure 6

How cosmological constraints $\Delta n_s$ depend on $k_{\min }$ (left panel) and $k_{\max }$ (right panel) in the MID model with the 21 cm experiments MWA (red/solid line), LOFAR (blue/short-dashed line), SKA (green/dotted line), and FFTT (cyan/long-dashed line). We plot $\Delta n_s$ in this example because it has the strongest dependence on $k_{\min }$ and $k_{\max }$ of all cosmological parameters. The quantity $2\pi /yB$ varies in redshift $z$ bins, so as the horizontal axis of the left panel, we use the overall scale ${\kappa }_{\min }\equiv k_{\min }\times (yB/2\pi )$ which is equal for all $z$ bins.

Figure 7

The $1\sigma$ errors for $m_{\nu }$ marginalized over vanilla parameters for various configurations $(R_0,R_{\mathrm{in}})$ of LOFAR (left panel), MWA (middle panel), and SKA (right panel). We made the same assumptions here as in Table  but assume only the OPT model.

Figure 8

Same as Fig. 7 but for the MID model. Figures are for LOFAR (left panel), MWA (middle panel), and SKA (right panel).

Figure 9

Cartoon showing how cosmological parameter measurement accuracy depends on various assumptions. The cases labeled merely “PESS” or “OPT” have the PESS/OPT ionization power spectrum modeling with MID assumptions for everything else.