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

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.

💡 Research Summary

This paper investigates the potential of forthcoming neutral‑hydrogen (HI) 21 cm intensity‑mapping (IM) surveys to place stringent constraints on f(R) modified‑gravity models, focusing on the Compton‑wavelength parameter B₀ that quantifies deviations from General Relativity (GR). After a concise motivation—highlighting the H₀ and σ₈ tensions that motivate departures from ΛCDM—the authors introduce the f(R) framework in the Jordan frame, derive the background Friedmann equations, and describe the scalar‑on degree of freedom. They adopt the quasi‑static approximation, parameterising the modified Poisson and anisotropy equations with the functions μ(a,k) and γ(a,k), which depend on B₀ (or equivalently the scalaron Compton wavelength λ, with B₀ = 2 H₀² λ²).

The observable is the redshifted 21 cm brightness temperature. Its mean value depends on the HI density Ω_HI and the Hubble rate, while fluctuations arise primarily from the HI density contrast (biased tracer of matter) and redshift‑space distortions (RSD). The authors retain only these two dominant terms, assume a scale‑independent linear HI bias b_HI, and expand the temperature field in spherical harmonics to obtain the angular power spectrum C_ℓ. The theoretical C_ℓ includes the standard ΛCDM contribution plus modifications induced by B₀ through μ and γ.

Two representative IM experiments are modelled in detail:

• BINGO – a single‑dish, drift‑scan telescope in Brazil covering 980–1260 MHz (0.13 ≲ z ≲ 0.45) over ~13 % of the sky, with 40 arcmin resolution, system temperature ≈70 K, and 10 MHz channel width.
• SKA1‑MID – a dish array in South Africa operating in two bands. Band 1 (350–1050 MHz, 0.36 ≲ z ≲ 3) and Band 2 (950–1410 MHz, 0.01 ≲ z ≲ 0.49). Band 2 is especially powerful, featuring a low system temperature ≈15 K, 5 000 deg² sky coverage, and finer angular resolution.

Thermal and shot‑noise contributions are computed for each configuration, yielding a noise power spectrum N_ℓ. The Fisher‑matrix formalism is then applied:

F_{ij}=∑_ℓ (2ℓ+1) f_sky