21-cm Background Anisotropies Can Discern Primordial Non-Gaussianity

The non-Gaussianity of initial perturbations provides information on the mechanism that generated primordial density fluctuations. We find that 21-cm background anisotropies due to inhomogeneous neutral hydrogen distribution prior to reionization captures information on primordial non-Gaussianity better than a high-resolution cosmic microwave background anisotropy map. An all-sky 21-cm experiment over the frequency range from 14 to 40 MHz with angular information out to a multipole of ${10}^5$ can limit the primordial non-Gaussianity parameter $f_{\mathrm{NL}}\lesssim 0.01$.

Figure 1

(a) The 21-cm anisotropy power spectrum ($\sqrt{l^2{C}_l/2\pi }$; solid line) and non-Gaussian squared 21-cm anisotropy—21-cm anisotropy power spectrum ($[l^3{X}_l/2\pi {]}^{1/3}$; see text for details) with the optimal filter applied [see Eq. (12)]. The dashed line is the signal related to the primordial bispectrum with $f_{\mathrm{NL}}=1$, while the dotted line is the noise bias $X_l^{\mathrm{grav}}$ from perturbation theory bispectrum under nonlinear gravitational clustering. The dot-dashed line shows the total noise spectrum, $[l^3{N}_l/2\pi {]}^{1/3}$, associated with the measurement of $X_l^{\mathrm{prim}}$. These spectra are calculated at $z=100$. (b) The cumulative signal-to-noise ratio for a detection of the non-Gaussian spectrum $X_l$ as a function of the multipole $l$ at $z=100$ (solid line) and at $z=30$ (dashed line). These estimates assume no detector noise with measurements limited by cosmic variance alone and with $f_{\mathrm{sky}}=1$.