Efficient computation of galaxy bias with neutrinos and other relics

Abstract

Cosmological data can be used to search for-and characterize-light particles in the standard model, if these populate our Universe. In addition to the well-known effect of these light relics in the background cosmology, usually parametrized through a change in the effective number N eff of neutrino species, these particles can become nonrelativistic at later times, affecting the growth of matter fluctuations due to their thermal velocities. An extensively studied example is that of massive neutrinos, which are known to produce a suppression in the matter power spectrum due to their free streaming. Galaxies, as biased traces of matter fluctuations, can therefore provide us with a wealth of information about both known and unknown degrees of freedom in the standard model. To harness this information, however, the galaxy bias has to be determined in the presence of massive relics, which is expected to vary with scale. Here we present the code RelicFast, which efficiently computes the scale-dependent bias induced by relics of different masses, spins, and temperatures, through spherical collapse and the peak-background split. Using this code, we find that, in general, the bias induced by light relics partially compensates the suppression of power, and should be accounted for in any search for relics with galaxy data. In particular, for the case of neutrinos, we find that both the normal and inverted hierarchies present a percent-level step in the Lagrangian bias, with a size scaling linearly with the neutrino-mass sum, in agreement with recent simulations. This effect persists at the subpercent level even if one defines the Eulerian bias with respect to dark matter only, suggesting that it has to be properly included in cosmological searches for the neutrino mass. RelicFast can compute halo bias in under a second, allowing for this effect to be properly included for different cosmologies, and light relics, at little computational cost.

Measuring dark matter-neutrino relative velocity on cosmological scales

“…where b is the galaxy bias and g is the stochastic noise term [28,29]. This is an approximation for the galaxy response with massive neutrinos, but accurate enough for the scales considered here [24,30]. Gravitational lensing and peculiar velocities are sensitive to the total matter field…”

Relativistic bias in neutrino cosmologies

“…For example due to the mismatch of the time coordinates used to describe the collapse and the time coordinate employed in a Boltzmann code, neutrinos would be evaluated at far too early times when they may still be relativistic and their impact on the collapse would be underestimated. We believe that these complications are responsible for the differences in the results we find compared to [19,20].…”

“…We believe that this difference is again rooted in the use of the closed Universe ansatz 1 . While [20] correctly includes the neutrino long modes in that case, a similar matching needs to be applied to the long modes of any species, except cold dark matter, i.e. including photons.…”

“…However, the simulation of neutrinos in general relativity is still a novel field and often relativistic corrections are neglected, see [16][17][18] for recent developments. In [19,20] a semi-analytic approach very close to our ansatz has been studied, however not considering all relativistic corrections. We aim to derive a treatment that includes all terms in general relativity required to describe light species such as neutrinos accurately.…”

“…A full comparison of the results of our work, relying on the Poisson gauge throughout, to those of[19] and[20] is difficult, since they do not include large-scale relativistic corrections and thus do not specify the gauge.…”