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Massive neutrinos suppress the growth of cosmic structure on small,non-linear, scales. It is thus often proposed that using statistics beyond thepower spectrum can tighten constraints on the neutrino mass by extractingadditional information from these non-linear scales. We study the informationcontent regarding neutrino mass at the field level, quantifying how much ofthis information arises from the difference in non-linear evolution between acosmology with 1 fluid (CDM) and 2 fluids (CDM + neutrinos). We do so byrunning two $N$-body simulations, one with and one without massive neutrinos;both with the same phases, and matching their linear power spectrum at a given,low, redshift. This effectively isolates the information encoded in the linearinitial conditions from the non-linear cosmic evolution. We demonstrate thatfor $k \lesssim 1\,h/{\rm Mpc}$, and for a single redshift, there is negligibledifference in the real-space CDM field between the two simulations. Thissuggests that all the information regarding neutrino mass is in the linearpower spectrum set by the initial conditions. Thus any probe based on the CDMfield alone will have negligible constraining power beyond that which exists atthe linear level over the same range of scales. Consequently, any probe basedon the halo field will contain little information beyond the linear power. Wefind similar results for the matter field responsible for weak lensing. We alsodemonstrate that there may be much information beyond the power spectrum in the3d matter field, however, this is not observable in modern surveys via darkmatter halos or weak lensing. Finally, we show that there is additionalinformation to be found in redshift space.

Beware of Fake $\nu$s: The Effect of Massive Neutrinos on the Nonlinear Evolution of Cosmic Structure