Combining galaxy and 21-cm surveys

Acoustic waves travelling through the early Universe imprint a characteristic scale in the clustering of galaxies, QSOs and intergalactic gas. This scale can be used as a standard ruler to map the expansion history of the Universe, a technique known as baryon acoustic oscillations (BAO). BAO offer a high-precision, low-systematics means of constraining our cosmological model. The statistical power of BAO measurements can be improved if the 'smearing' of the acoustic feature by non-linear structure formation is undone in a process known as reconstruction. In this paper, we use low-order Lagrangian perturbation theory to study the ability of 21-cm experiments to perform reconstruction and how augmenting these surveys with galaxy redshift surveys at relatively low number densities can improve performance. We find that the critical number density which must be achieved in order to benefit 21-cm surveys is set by the linear theory power spectrum near its peak, and corresponds to densities achievable by upcoming surveys of emission line galaxies such as eBOSS and DESI. As part of this work, we analyse reconstruction within the framework of Lagrangian perturbation theory with local Lagrangian bias, redshift-space distortions, k-dependent noise and anisotropic filtering schemes