Primordial non-gaussianity from the bispectrum of 21-cm fluctuations in the dark ages

TL;DR

This study demonstrates that 21-cm brightness-temperature fluctuations from the dark ages offer a powerful probe of primordial non-Gaussianity by exploiting a vast number of small-scale modes. It develops a rigorous flat-sky bispectrum framework to separate primary PNG signals from dominant secondary bispectra arising from non-linear evolution and non-linear brightness-temperature mappings, showing strong degeneracies between them. Through a Fisher analysis that marginalizes over smooth redshift-dependent nuisance parameters, the authors quantify the impact on PNG constraints and implement a tomographic approach to recover sensitivity. They forecast that a cosmic-variance-limited experiment covering $30 \lesssim z \lesssim 100$ with high angular and frequency resolution could reach $\sigma_{f_{\rm NL}}^{\rm local} \sim 0.03$, $\sigma_{f_{\rm NL}}^{\rm equil} \sim 0.04$, and $\sigma_{f_{\rm NL}}^{\rm ortho} \sim 0.03$, representing a substantial improvement over current CMB limits and testing inflationary consistency relations.

Abstract

A measurement of primordial non-gaussianity will be of paramount importance to distinguish between different models of inflation. Cosmic microwave background (CMB) anisotropy observations have set unprecedented bounds on the non-gaussianity parameter f_NL but the interesting regime f_NL <~ 1 is beyond their reach. Brightness-temperature fluctuations in the 21-cm line during the dark ages (z ~ 30-100) are a promising successor to CMB studies, giving access to a much larger number of modes. They are, however, intrinsically non-linear, which results in secondary non-gaussianities orders of magnitude larger than the sought-after primordial signal. In this paper we carefully compute the primary and secondary bispectra of 21-cm fluctuations on small scales. We use the flat-sky formalism, which greatly simplifies the analysis, while still being very accurate on small angular scales. We show that the secondary bispectrum is highly degenerate with the primordial one, and argue that even percent-level uncertainties in the amplitude of the former lead to a bias of order Delta f_NL ~ 10. To tackle this problem we carry out a detailed Fisher analysis, marginalizing over the amplitudes of a few smooth redshift-dependent coefficients characterizing the secondary bispectrum. We find that the signal-to-noise ratio for a single redshift slice is reduced by a factor of ~5 in comparison to a case without secondary non-gaussianities. Setting aside foreground contamination, we forecast that a cosmic-variance-limited experiment observing 21-cm fluctuations over 30 < z < 100 with a 0.1-MHz bandwidth and 0.1-arcminute angular resolution could achieve a sensitivity of order f_NL[local] ~ 0.03, f_NL[equilateral] ~ 0.04, and f_NL[orthogonal] ~ 0.03.

Figures (8)

• Figure 1: Coefficients of the approximate decomposition of the gas-temperature fluctuations as a quadratic function of baryon density fluctuations: $\delta_{T_{\rm gas}}(\boldsymbol{x}, z) \approx C_1(z) \delta_b^{(1)}(\boldsymbol{x}, z) + C_2(z) [\delta_b^{(1)}(\boldsymbol{x}, z)]^2 + C_2'(z) \delta_b^{(2)}(\boldsymbol{x}, z)$. At high redshift, Compton heating is efficient and maintains $T_{\rm gas} = T_{\rm cmb}$, with negligible fluctuations, so $C_1 \approx C_2 \approx C_2' \approx 0$. At low redshift, the gas decouples thermally from the CMB and starts cooling down adiabatically, asymptoting towards $T_{\rm gas} \propto n_b^{2/3}$, which implies $C_1 \approx C_2' \rightarrow 2/3$ and $C_2 \rightarrow -1/9$.
• Figure 2: Coefficients of the approximate decomposition of the 21-cm brightness temperature given in Eq. \ref{['eq:T21']}, in mK. In solid black we plot $\overline{T}_{21}$, in blue dashed $\alpha=\partial T_{21}/\partial \delta_b^{(1)}$, in red dotted $\beta=\frac{1}{2} \partial^2 T_{21}/\partial \delta_b^2$, and in purple dot-dashed $\gamma = \partial T_{21}/\partial \delta_b^{(2)}$.
• Figure 3: Flat-sky power spectrum $C_{\ell}$ in the limit of infinitely narrow window function, for redshifts (top to bottom) $z=50$ (blue), $z=100$ (black) and $z=30$ (red). We also show the $C_{\ell}$ at redshift $z=50$ for a Gaussian window function of width $0.1$ MHz (blue dashed) and width of 1 MHz (blue dotted).
• Figure 4: Bispectra of 21-cm brightness-temperature fluctuations resulting from secondary non-gaussianities and different shapes of primordial non-gaussianity, with $f_{\rm NL} = 1$, at $z = 50$. The top panel shows the bispectra for equilateral triangles ($\ell \equiv \ell_1=\ell_2=\ell_3$). The bottom panel shows the bispectra for squeezed triangles ($\ell \equiv \ell_1=\ell_2\gg \ell_3=\ell/50$). In dashed blue we plot local, in dotted orange equilateral and in dash-dotted green orthogonal non-gaussianity. In solid black we plot the secondary bispectrum. The bispectra are computed in the flat-sky approximation for an infinitesimally narrow redshift slice.
• Figure 5: Signal-to-noise ratio (SNR) for PNG of the local type with $f_{\rm NL} = 1$, for a single narrow redshift slice at $z = 50$ and assuming $f_{\rm sky} = 1$. The blue dashed curve shows $(F_{00})^{1/2}$, the SNR obtained if one neglected secondary non-gaussianity. The black solid and red dotted curves show $[(F^{-1})_{00}]^{-1/2}$, the SNR after marginalization over the unknown residual amplitudes of the secondary bispectrum, as a function of $\ell_{\max}$ (black solid) and as a function of $\ell_{\min}$ at fixed $\ell_{\max} = 10^5$ (red dotted).