Abstract
Using a suite of hydrodynamical simulations with cold dark matter, baryons,
and neutrinos, we present a detailed study of the effect of massive neutrinos
on the 1-D and 3-D flux power spectra of the Lyman-$\alpha$ (Ly$\alpha$)
forest. The presence of massive neutrinos in cosmology induces a scale- and
time-dependent suppression of structure formation that is strongest on small
scales. Measuring this suppression is a key method for inferring neutrino
masses from cosmological data, and is one of the main goals of ongoing and
future surveys like eBOSS, DES, LSST, Euclid or DESI. The clustering in the
Ly$\alpha$ forest traces the quasi-linear power at late times and on small
scales. In combination with observations of the cosmic microwave background,
the forest therefore provides some of the tightest constraints on the sum of
the neutrino masses. However there is a well-known degeneracy between $\Sigma
m_\nu$ and the amplitude of perturbations in the linear matter power
spectrum. We study the corresponding degeneracy in the 1-D flux power spectrum
of the Ly$\alpha$ forest, and for the first time also study this degeneracy in
the 3-D flux power spectrum. We show that the non-linear effects of massive
neutrinos on the Ly$\alpha$ forest, beyond the effect of linear power amplitude
suppression, are negligible, and this degeneracy persists in the Ly$\alpha$
forest observables to a high precision. We discuss the implications of this
degeneracy for choosing parametrisations of the Ly$\alpha$ forest for
cosmological analysis.
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