Cosmological forecast from the full-sky angular power spectrum and bispectrum of 21cm intensity mapping

Abstract

We compute the full-sky angular power spectrum and bispectrum, along with their Fisher matrices, to forecast constraints on cosmological parameters for the BINGO and SKA1-MID Band 2 radio telescopes. This represents the first forecast analysis using the full-sky relativistic bispectrum in redshift space for these surveys. Our results show that the second-order velocity contribution, often neglected under the Limber approximation, accounts for approximately $24\%$ of the total signal at low redshifts, indicating that it must be included for accurate modeling. Using these forecasts, we find that while the bispectrum provides constraints comparable to the angular power spectrum for $Λ$CDM and ${\rm w}$CDM models, it becomes a powerful probe of dynamical dark energy. Restricting the analysis to linear scales, we show that the inclusion of the bispectrum yields a substantial improvement in the determination of the Chevallier-Polarski-Linder (CPL) parameters. In particular, the joint analysis of the bispectrum, power spectrum, and Planck CMB data improves constraints on ${\rm w}_0$ and ${\rm w}_a$ by over $70\%$, and the Hubble parameter $h$ by approximately $60\%$. These results underscore the importance of relativistic bispectrum for breaking parameter degeneracies and probing the nature of dark energy with upcoming large-scale structure surveys.

Figures (4)

• Figure 1: The six components of the angle-averaged 21cm bispectrum at $z = 0.3$, shown for equilateral, squeezed, folded, and staggered triangle configurations. The second-order velocity term ($v^{(2)^{\prime}}$) provides a significant contribution, while the final two components remain negligible in all configurations.
• Figure 2: Exact (solid) and approximate (dashed) total angle-averaged 21cm bispectrum at $z = 0.01, 0.127, 0.3, 0.45$, and $0.49$, shown for the equilateral, squeezed, folded, and staggered triangle configurations. The maximum multipole $\ell_{\rm max}$ is given by the nonlinear cutoff scale $\ell_{\rm max}^{\rm nl}$ at each redshift, except for $z=0.01$, where $\ell_{\rm max}$ is extrapolated to higher multipoles for better visualization. The approximate bispectrum is obtained using the averaged fractional parameter $r = 0.24$.
• Figure 3: Specification of the multipole ranges [$\ell_{\text{min}}$, $\ell_{\text{max}}$] adopted for the SKA1-MID Band 2 and BINGO surveys. The lower bound, $\ell_{\text{min}}$, accounts for the loss of large-scale radial modes during foreground subtraction. We define $\ell_{\text{max}}$ to be determined by either the onset of the non-linear regime or the instrumental resolution.
• Figure 4: Forecasted 68$\%$ and 95$\%$ confidence contours for the CPL parameters ${\rm w}_0$, ${\rm w}_a$, and the Hubble constant $h$. The left panel corresponds to BINGO and the right panel to SKA1-MID band 2. Constraints are derived using the $C_\ell$, $B_{\ell}$, Planck, $C_\ell + \text{Planck}$, and $B_{\ell} + \text{Planck}$ statistics.