Deconstructing the neutrino mass constraint from galaxy redshift surveys

The total mass of neutrinos can be constrained in a number of ways using galaxy redshift surveys. Massive neutrinos modify the expansion rate of the Universe, which can be measured using baryon acoustic oscillations (BAOs) or the Alcock-Paczynski (AP) test. Massive neutrinos also change the structure growth rate and the amplitude of the matter power spectrum, which can be measured using redshift-space distortions (RSD). We use the Fisher matrix formalism to disentangle these information sources, to provide projected neutrino mass constraints from each of these probes alone and to determine how sensitive each is to the assumed cosmological model. We isolate the distinctive effect of neutrino free-streaming on the matter power spectrum and structure growth rate as a signal unique to massive neutrinos that can provide the most robust constraints, which are relatively insensitive to extensions to the cosmological model beyond $\Lambda$CDM. We also provide forecasted constraints using all of the information contained in the observed galaxy power spectrum combined, and show that these maximally optimistic constraints are primarily limited by the accuracy to which the optical depth of the cosmic microwave background, $\tau$, is known.