We investigate the prospects for constraining alternative theories of gravity with a typical near-term, low-budget 21-cm intensity mapping experiment. We derive the 21-cm brightness temperature perturbation consistently in linear theory, including all line-of-sight and relativistic effects. We uncover new terms that are a small correction on large scales, analogous to those recently found in the context of galaxy surveys. We then perform a Fisher matrix analysis of the $B_0$ parametrization of $f(R)$ gravity, where $B_0$ is proportional to the square of the Compton wavelength of the scalaron. We find that our 21-cm survey, in combination with CMB information from Planck, will be able to place a 95% upper limit of $7\times {10}^{-5}$ on $B_0$ in flat models with a $\Lambda \mathrm{CDM}$ expansion history, improving on current cosmological constraints by several orders of magnitude. We argue that this constraint is limited by our ability to model the mildly nonlinear regime of structure formation in modified gravity. We also perform a model-independent principal component analysis on the free functions introduced into the field equations by modified gravity, $\mu$ and $\Sigma$. We find that 20–30 modes of the free functions will be “well-constrained” by our combination of observables, the lower and upper limits dependent on the criteria used to define the “goodness” of the constraint. These constraints are found to be robust to uncertainties in the time dependence of the bias. Our analysis reveals that our observables are sensitive primarily to temporal variations in $\Sigma$ and scale variations in $\mu$. We argue that the inclusion of 21-cm intensity maps will significantly improve constraints on any cosmological deviations from general relativity in large-scale structure in a very cost-effective manner.

• Received 4 December 2012

DOI:https://doi.org/10.1103/PhysRevD.87.064026