Can Dark Matter Be Lighter Than The Tremaine-Gunn Lower Bound? (Cosmology / Astronomy)

While the astrophysical evidence for dark matter (DM) is overwhelming, its particle nature has evaded detection. It is generally held that DM cannot be lighter than ∼ 10¯22 eV below which point the de Broglie wavelength of DM becomes larger than observed DM structures. On the other end DM heavier than ∼ 1067 eV (∼ 10 M) would cause significant tidal effects on visible structures. This represents the broadest allowed range of DM mass.

In 1979, Tremaine and Gunn (TG) pointed out that fermionic DM lighter than ∼ 100 eV would not be contained within a galactic halo, immediately ruling out about 24 orders of magnitude of parameter space for fermions. Modern treatments looking at dwarf spheroidal galaxies find similar bounds on fermionic DM m ≳ 50−190 eV.

Now, Davoudiasl and colleagues in their recent paper note that this bound can be significantly weakened if there are many, N_F, distinct species of fermionic dark matter whose masses are nearly degenerate. For very large number of species the momentum of the matter stored within any one of the fermionic species will not exceed the escape velocity from galactic structures and the mass scale of the fermions can be brought down to well below O(eV), often considered the ultralight regime. They thus referred to this possibility as ultralight fermionic dark matter (UlFDM).

If one allows for the dark matter population to comprise a large number NF of fermions, the phase space restrictions which depend on spin statistics of identical fermions i.e. Pauli’s exclusion principle, are avoided and the mass lower bound can be relaxed with NF ^ (–1/4). “

— wrote authors of the study

Their ultralight fermion dark matter scenario has a number of striking phenomenological consequences. Due to the enormous number of species one could expect gravitational effects that are normally completely negligible. These include detectable effects from graviton exchange at the TeV scale, such as in collider experiments or via high energy cosmic rays, as well as accelerated evaporation of solar-mass black holes on astronomical time scales.

We find that the LHC constrains the number of distinct species, bosons or fermions lighter than ∼ 500 GeV, to be N ≲ 1062. This, in particular, implies that roughly degenerate fermionic dark matter must be heavier than ∼ 10¯13 eV, which thus relaxes the Tremaine-Gunn bound by ∼ 16 orders of magnitude.

— told Davoudiasl, first author of the study

They considered these and other effects, and found that they roughly yield the constraint N ≲ 1062, for which one could accommodate fermionic dark matter as light as 10¯13 eV. Depending on the assumptions of the underlying model, stronger bounds could apply, for example originating from the possibility of gravity-mediated fast proton decay or non-standard neutrino oscillations, as well as possible modifications of Newton’s constant.

A summary of several constraints relevant for any new physics model assuming a large number of species with no SM interactions; shaded regions are ruled out. All constraints apply regardless of spin, unless specified. © Davoudiasl et al.

Their work illustrated that departure from a monolithic picture of fermionic dark matter, by allowing a large number of species, could open novel and exciting phenomenological possibilities that deserve attention, as the decades-long search for clues to the identity of dark matter continues.

Reference: Hooman Davoudiasl, Peter B. Denton, David A. McGady, “Ultralight Fermionic Dark Matter”, Phys. Rev. D 103, 055014 – Published 19 March 2021.

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