How accurately can 21 cm tomography constrain cosmology?

TL;DR

This work develops a Fisher-mmatrix framework to forecast cosmological constraints from 21 cm tomography across varied assumptions about ionization physics, reionization histories, and instrument design. It shows that modeling the ionization power spectra ($\mathscr{P}_{xx}$, $\mathscr{P}_{x\delta}$) dominates forecast precision, with OPT and MID scenarios yielding substantial improvements when combined with Planck data, while the conservative PESS approach greatly attenuates gains. The study identifies quasi-giant-core telescope layouts, extended redshift coverage, and effective foreground removal as key levers for tightening constraints on spatial curvature $\Omega_k$, neutrino mass $m_\nu$, and the running of the spectral index $\alpha$, projecting up to two orders of magnitude improvement over Planck for some parameters. It highlights the need for improved EoR modeling and realistic end-to-end instrument simulations to realize the full potential of 21 cm cosmology.

Abstract

There is growing interest in using 3-dimensional neutral hydrogen mapping with the redshifted 21 cm line as a cosmological probe, as it has been argued to have a greater long-term potential than the cosmic microwave background. 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. We cover assumptions related to modeling of the ionization power spectrum and associated nonlinearity, experimental specifications like array layout and noise, cosmological assumptions about reionization history and inter-galactic medium (IGM) evolution, and assumptions about astrophysical foregrounds. We derive simple analytic approximations for how various assumptions affect the results, and find that ionization power modeling is most important, followed by array layout (crudely, the more compact, the better). We also present an accurate yet robust method for measuring cosmological parameters in practice, separating the physics from the astrophysics by exploiting both gravitationally induced clustering anisotropy and the fact that the ionization power spectra are rather smooth functions that can be accurately fit by 7 phenomenological parameters. For example, a future square kilometer array optimized for 21 cm tomography could improve the sensitivity of the Planck CMB satellite to spatial curvature and neutrino masses by up to two orders of magnitude, to Delta-Omega_k ~ 0.0002 and Delta m_nu ~ 0.007 eV, and give a 4 sigma detection of the spectral index running predicted by the simpliest inflation models.

Figures (9)

• Figure 1: 21 cm tomography can potentially map most of our observable universe (light blue/light grey), 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 grey).
• 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 McQuinn:2007dy. Dashed (green) lines are fitting curves of our parametrization. Dot-dashed (red) lines are best fits using the parametrization suggested by Santos and Cooray Santos:2006fp . Top panels: $\mathscr{P}_{xx}/\mathscr{P}_{\delta\delta}=P_{\rm xx}/(\bar{x}_{\rm H}^{2} P_{\delta\delta})$. Bottom panels: $\mathscr{P}_{x\delta}/\mathscr{P}_{\delta\delta}=P_{{\rm x}\delta}/(\bar{x}_{\rm H} P_{\delta\delta})$. From left to right: $z=9.2,\,8.0,\,7.5,\,7.0$ ($\bar{x}_{\rm i}=0.10,\, 0.30,\, 0.50,\, 0.70$ 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 $R_0<r<R_{in}$ where $R_{in}$ 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 $R_{in}< r< R_{out}$, where $R_{out}$ is the outer annulus radius. When $R_0$ is decreased ($R_0=0.7/0.5/0.3\times R_0^{\rm max}$) with $R_{in} = 3.0\times R_0^{\rm max}$ fixed (left panels), the density in the core falls off slower (blue/red/green curves). When $R_{in}$ is decreased ($R_{in}=4.0/3.0/2.0\times R_0^{\rm max}$) with $R_0=0.5\times R_0^{\rm max}$ fixed (right panels), the density in the core also falls off less steep (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/grey regions can be measured with good signal-to-noise from the nucleus and core of an array, while the cyan/light-grey regions are measured only with the annulus and have so poor signal-to-noise that they hardly contribute to cosmological parameter constraints.
• Figure 5: Relative 1$\sigma$ error for measuring $\mathscr{P}_{\delta\delta}(k)$ with the PESS model by observing a 6MHz band that is centered at $z=8$ with MWA (red/solid), LOFAR (blue/short-dashed), SKA (green/dotted) and FFTT (cyan/long-dashed). The step size is $\Delta \ln k \approx 0.10$.