Cosmological Parameter Estimation Using 21 cm Radiation from the Epoch of Reionization

TL;DR

This work investigates how 21 cm radiation from the Epoch of Reionization can be used to constrain cosmological parameters, exploiting redshift-space distortions that create a non-spherical 3D power spectrum decomposed into $P_{\\mu^0}$, $P_{\\mu^2}$, and $P_{\\mu^4}$ terms and potential AP signatures. It combines a physically motivated semi-analytic reionization model (FZH04) with a detailed Fisher-matrix framework that accounts for interferometric visibilities, detector noise, sample variance, and realistic foreground subtraction to forecast sensitivities for MWA, LOFAR, and SKA. The paper shows that, under favorable conditions (density fluctuations dominating and late reionization), upcoming 21 cm experiments can meaningfully improve cosmological parameter constraints, especially when combined with Planck, and may probe small-scale structure beyond CMB limits; in more challenging ionization scenarios or with strong spin-temperature fluctuations, achieving competitive cosmological constraints becomes substantially harder. Overall, the study highlights both the rich cosmological information encoded in the 21 cm power spectrum and the critical instrumental and foreground requirements needed to realize it as a competitive cosmological probe.

Abstract

A number of radio interferometers are currently being planned or constructed to observe 21 cm emission from reionization. Not only will such measurements provide a detailed view of that epoch, but, since the 21 cm emission also traces the distribution of matter in the Universe, this signal can be used to constrain cosmological parameters at 6 < z < 20. The sensitivity of an interferometer to the cosmological information in the signal may depend on how precisely the angular dependence of the 21 cm 3-D power spectrum can be measured. Utilizing an analytic model for reionization, we quantify all the effects that break the spherical symmetry of the 3-D 21 cm power spectrum and produce physically motivated predictions for this power spectrum. We find that upcoming observatories will be sensitive to the 21 cm signal over a wide range of scales, from larger than 100 to as small as 1 comoving Mpc. We consider three methods to measure cosmological parameters from the signal: (1) direct fitting of the density power spectrum to the signal, (2) using only the velocity field fluctuations in the signal, (3) looking at the signal at large enough scales such that all fluctuations trace the density field. With the foremost method, the first generation of 21 cm observations should moderately improve existing constraints on cosmological parameters for certain low-redshift reionization scenarios, and a two year observation with the second generation interferometer MWA5000 can improve constraints on Omega_w, Omega_m h^2, Omega_b h^2, Omega_nu, n_s, and alpha_s. If the Universe is substantially ionized by z = 12 or if spin temperature fluctuations are important, we show that it will be difficult to place competitive constraints on cosmological parameters with any of the considered methods.

Figures (12)

• Figure 1: The $\mu$ decomposition of the signal (see equation \ref{['pseqn']}) for $\bar{x}_i = 0.1$ and $0.7$, corresponding to $z = 13.5$ and $9$ in the $\zeta = 12$ model. The thick solid, thick dashed and thick dot-dashed curves show $P_{\mu^0}$, $P_{\mu^2}$, and $P_{\mu^4}$, respectively. The three thin solid curves show $P_{f(\mu, k)}$, calculated using equation (\ref{['bad2eqn']}) with $\mu^2 = 0.0, 0.5$ and $1.0$ (in order of increasing amplitude).
• Figure 2: Contours of constant $k^3 P_{\Delta T}(k)$ for the same signal as in Figure \ref{['pscompfig']}. The horizontal axis is the LOS direction, and the vertical axis is the transverse direction. The coordinate transformation $(k_{\perp}, k_{||}) \rightarrow \log(k/(0.01 ~{\rm Mpc}^{-1})) (\sin(\theta), \cos(\theta))$ preserves circles of constant power.
• Figure 3: Dimensionless power spectrum $k^3 \,P_{\Delta T}/2 \pi^2$ for $\mu^2$ equal to $0.0, \, 0.5,$ and $1.0$ ( solid, dash-dot, and dashed lines, respectively) for four times during reionization in the $\zeta= 12$ model, corresponding to $z =$ 9, 9.8, 13.5 and 20 (in order of decreasing $\bar{x}_i$). The signal is most asymmetric at scales where density fluctuations dominate.
• Figure 4: Integrated number of Fourier pixels $N_{S/N > 1}(k)$ with $k' < k$ that have a ratio of the RMS signal to the RMS detector noise that is greater than unity for a $1000$ hr observation with $B = 6 ~ {\rm MHz}$. We use the specifications given in Table \ref{['table1']} and in § \ref{['detectors']} for MWA ( dashed curve), LOFAR ( dot-dashed curve), and SKA ( solid curve). These curves do not include pixels with $k < 2 \pi/ y$, since foregrounds will contaminate these pixels substantially. The 21 cm signal for this calculation is from a fully neutral medium in which $T_s \gg T_{\rm CMB}$. If the universe is partially ionized at $z = 8$, the signal can be both larger and smaller than this (see Fig. \ref{['fig:errors']}). By a redshift of $12$, only SKA will have any high S/N pixels.
• Figure 5: Fraction of Fourier pixels for MWA ( dashed curve), LOFAR ( dot-dashed curve), and SKA ( solid curve) that are "imaged"--- that is, they have a ratio of RMS signal (assuming a neutral universe) to RMS detector noise that is greater than unity---after $1000$ hr of observation in a Fourier shell of radius $k$. The hatched vertical line marks the depth of this 6 MHz observation at $z = 8$. Scales to the left of this should be wiped out by foregrounds. LOFAR can image a substantially higher fraction of pixels at the relevant $k$ than MWA, and SKA can image nearly all of its pixels up to $k = 0.3 \, {\rm Mpc}^{-1}$.