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

TLDR: In this paper, the authors quantify all the effects that break the spherical symmetry of the three-dimensional 21 cm power spectrum and show that it will be difficult to place competitive constraints on cosmological parameters with any of the considered methods.

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. The sensitivity of an interferometer to the cosmological information in the signal may depend on how precisely the angular dependence of the 21 cm three-dimensional power spectrum can be measured. Using an analytic model for reionization, we quantify all the effects that break the spherical symmetry of the three-dimensional 21 cm 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. Next, 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, and (3) looking at the signal at large enough scales 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 2 yr observation with the second-generation interferometer MWA5000 in combination with the CMB telescope Planck could improve constraints on Ω_w, Ω_(m)h^2, Ω_(b)h^2, Ω_ν, n_s, and α_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

Fig. 3.—Dimensionless power spectrum k3P T /2 2 for 2 equal to 0.0, 0.5, and 1.0 (solid, dot-dashed, and dashed lines, respectively) for four times during reionization in the ¼ 12 model, corresponding to z ¼ 9, 9.8, 13.5, and 20 (in order of decreasing x̄i). The signal is most asymmetric at scales where density fluctuations dominate.

Fig. 4.—Integrated number of Fourier pixels NS=N>1 kð Þ with k 0< 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 ¼ 6 MHz. We use the specifications given in Table 1 and in x 5 for MWA (dashed curve), LOFAR (dot-dashed curve), and SKA (solid curve). These curves do not include pixels with k < 2 /y, since foregrounds will contaminate these pixels substantially. The 21 cm signal for this calculation is from a fully neutral medium in which Ts 3TCMB. If the universe is partially ionized at z ¼ 8, the signal can be both larger and smaller than this (see Fig. 6). By a redshift of 12, only SKAwill have any high-S/N pixels. [See the electronic edition of the Journal for a color version of this figure.]

Fig. 5.—Fraction of Fourier pixels for MWA (dashed curve), LOFAR (dotdashed 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 ¼ 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 ¼ 0:3 Mpc 1. [See the electronic edition of the Journal for a color version of this figure.]

Fig. 6.—Detector noise plus sample variance errors for a 1000 hr observation on a single field in the sky, assuming perfect foreground removal, for MWA (thick dashed curve), LOFAR (thick dot-dashed curve), and SKA (thick solid curve), using the specifications given in Table 1 and in x 5 and for bin sizes of k ¼ 0:5k. These errors are for the spherically averaged signal (see text for the discussion of this point). The hatched line in the middle panel represents MWA with a flat distribution of antennae rather than the fiducial r 2 distribution. The detector noise dominates over sample variance for these sensitivity curves on almost all scales. The thin solid curve represents the spherically averaged signal for x̄iT1 and Ts 3TCMB. We use this curve to calculate the sample variance error. For comparison, the thin dashed curves show the signal from the FZH04modelwhen x̄i is equal to 0.20, 0.55, and 0.75 for z ¼ 12, 8, and 6, respectively. [See the electronic edition of the Journal for a color version of this figure.]

Fig. 9.—Cosmic variance plus detector noise errors on the large-scale modes of the spherically averaged power spectrum for SKA (thick error bars) and MWA5000 (thin error bars) after 1000 hr of observation in a 6 MHz band. We accentuate the wiggles in P T (k) by subtracting a power spectrum that does not have baryonic wiggles, Pnw T kð Þ. The vertical hatched line indicates the size of a 6 MHz box, approximately where we expect foregrounds to swamp the signal. The second generation of interferometers will be able to detect the wiggles at a few significance level. MWA5000 is more sensitive than SKA to these features because of its larger FOV. The signal here is for x̄iT1; the presence of H ii bubbles may enhance these wiggles (x 6.3). [See the electronic edition of the Journal for a color version of this figure.]

TABLE 2 Errors on Cosmological Parameter Estimates When Density Fluctuations Dominate the 21 cm Signal