Testing General Relativity with 21 cm intensity mapping

TL;DR

This paper evaluates the potential of 21 cm intensity mapping experiments to test and constrain alternative theories of gravity, especially f(R) models, with significant improvements over current limits.

Contribution

It derives the 21 cm brightness temperature perturbation including relativistic effects and performs Fisher and principal component analyses to assess constraints on modified gravity parameters.

Findings

21 cm surveys can constrain B_0 to 7 x 10^{-5} with Planck data.

20-30 modes of free functions in modified gravity can be well-constrained.

Constraints are robust to bias uncertainties and sensitive to specific modifications in gravity.

Abstract

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.