Forecast on $f(R)$ Gravity with HI 21cm Intensity Mapping Surveys

TL;DR

This paper investigates whether late-time deviations from General Relativity in $f(R)$ gravity, parameterized by the present-day Compton-wavelength $B_0$, can be constrained with low-redshift HI 21 cm intensity mapping. Using Fisher-matrix forecasts for upcoming surveys BINGO and SKA1-MID (Bands 1 and 2), alone and with Planck CMB priors, the authors model the 21 cm angular power spectra incorporating density and redshift-space distortion contributions and the modified gravity functions $\mu(a,k)$ and $\gamma(a,k)$. They find that BINGO alone constrains $B_0$ at $\sigma(B_0)\approx 2.3\times 10^{-6}$, while SKA1-MID Band 2 reaches $\sigma(B_0)\approx 6.4\times 10^{-8}$; combining with Planck priors dramatically tightens the limits, with Planck+SKA Band 2 giving $\sigma(B_0)\approx 3.8\times 10^{-8}$. The results indicate that low-redshift 21 cm IM, especially when paired with CMB data, can significantly test GR on cosmological scales, with the dominant information coming from large-angular-scale modes and growth signatures of the scalaron.

Abstract

Modified gravity theories offer a well-motivated extension of General Relativity and provide a possible explanation for the late-time accelerated expansion of the Universe. Among them, $f(R)$ gravity represents a minimal and theoretically appealing class, characterized by the Compton wavelength parameter $B_0$, which quantifies deviations from General Relativity. In this work, we explore the capability of future neutral hydrogen (HI) 21 cm intensity mapping (IM) observations to constrain $f(R)$ gravity at low redshifts. We perform Fisher-matrix forecasts for $B_0$ and standard cosmological parameters using upcoming 21 cm IM experiments, including BINGO and SKA1-MID (Band 1 and Band 2), both individually and in combination with Planck cosmic microwave background (CMB) priors. We find that even near-term experiments such as BINGO are able to place nontrivial bounds on $B_0$, $σ(B_0)\simeq 2.27\times 10^{-6}$, while SKA1-MID yields substantially tighter constraints, with SKA Band 2 providing the strongest sensitivity among the considered configurations, $σ(B_0)\simeq 6.37\times 10^{-8}$. We further demonstrate that the combination of low-redshift 21 cm IM data with CMB observations efficiently breaks degeneracies with background cosmological parameters and leads to a significant improvement in the constraints on $B_0$. These results highlight the potential of future HI intensity mapping surveys, in combination with CMB measurements, to provide stringent tests of General Relativity on cosmological scales.

Figures (5)

• Figure 1: Angular power spectra of the HI 21 cm signal at redshift $z=0.27$ with a channel bandwidth of $9.33\,\mathrm{MHz}$. Left panel: auto-spectra for different values of the $f(R)$ parameter $B_0$, where $B_0=0$ corresponds to the $\Lambda$CDM case. Right panel: fractional deviations of the $f(R)$ spectra relative to $\Lambda$CDM. Larger values of $B_0$ lead to stronger departures from $\Lambda$CDM, especially on small angular scales.
• Figure 2: Angular power spectra of the HI 21 cm signal, thermal noise, and shot noise for BINGO (top left), SKA1-MID Band 1 (top right), and Band 2 (bottom), evaluated at multiple redshift bins. The HI signal dominates over instrumental noise on large angular scales. The thermal noise contribution is smallest for SKA Band 2.
• Figure 3: Marginalized one- and two-dimensional confidence regions (68% and 95%) for selected cosmological parameters and the $f(R)$ gravity parameter $B_0$. Results are shown for BINGO (top left), SKA1-MID Band 1 (top right), and Band 2 (bottom), both with and without Planck CMB priors. The inclusion of Planck data significantly reduces parameter degeneracies and tightens the constraints.
• Figure 4: Marginalized 68% and 95% confidence contours in the $B_0$–$h$ plane for BINGO (left), SKA1-MID Band 1 (middle), and Band 2 (right). Results are shown for IM-only forecasts and in combination with Planck priors. The strong degeneracy between $B_0$ and $h$ present in IM-only surveys is efficiently broken when CMB information is included.
• Figure 5: Ratios of the marginalized parameter uncertainties obtained with a maximum multipole $\ell_{\rm max}$ to those obtained with $\ell_{\rm max}=400$, as functions of $\ell_{\rm max}$. Results are shown for different survey configurations. A dual $y$-axis is adopted to display parameters with different amplitudes of $\sigma(\theta_i)/\sigma(\theta_i;\ell_{\rm max}=400)$. The figure illustrates the convergence of parameter constraints as smaller angular scales are progressively included, showing that most constraints saturate at $\ell_{\rm max}\sim300$--$400$.