Testing General Relativity with 21 cm intensity mapping
  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 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 x 10^{-5} on B_0 in flat models with a LCDM 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 non-linear 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.
