Bounds on very weakly interacting ultra light scalar and pseudoscalar dark matter from quantum gravity

Abstract

In this paper we consider very weakly interacting and ultra light scalar and pseudoscalar dark matter candidates. We show that quantum gravity has important implications for such models and that the masses of the singlet scalar and pseudoscalar fields must be heavier than $$3\times 10^{-3}$$3×10-3 eV. However, if they are gauged, their masses could be much lighter and as light as $$10^{-22}\, \mathrm{eV}$$10-22eV. The existence of new gauge forces in the dark matter sector can thus be probed by atomic clocks or quantum sensors experiments.

Theoretical bounds on dark matter masses

“…where M P = 2.4 × 10 18 GeV is the reduced Planck scale, φ is the scalar dark matter field, and F µν is the electromagnetic field tensor. We note that there are solid arguments showing that the Wilson coefficient c 1 is of order one [21].…”

“…We consider local operators that are generated by non-perturbative quantum gravity effects (see e.g. [19][20][21][22][23][24][25][26][27]):…”

“…The results from the Eöt-Wash torsion pendulum experiment that searches for fifth forces [10][11][12][13][14][15][16][17][18] imply that m φ 10 −3 eV [19][20][21]. The same operator can lead to the decay of the dark matter scalar [28,29] with a decay width Γ ∼ m 3 φ /(4πM 2 P ) and lead to an upper bound m φ 10 7 eV from the requirement that the dark matter candidate lives long enough to still be present in today's universe.…”

QSNET, a network of clock for measuring the stability of fundamental constants

“…One expects on very general grounds that quantum gravity will generate an interaction between any scalar field φ and regular matter with d (i) j ∼ O(1) whether such a coupling exists or not when gravity decouples. 10,[12][13][14][15] However, very light scalar fields coupling linearly to regular matter (i.e. dimension five operators) are essentially ruled out by the Eöt-Wash torsion pendulum experiment [16][17][18][19] for d…”

“…10, 12-15 QSNET will therefore provide a very important test of quantum gravity. 10,[12][13][14][15] If a very light neutral scalar field with linear coupling to regular matter was found with QSNET, we would learn that dimension 5 operators are not generated by quantum gravity. On the other hand, non-linear couplings are far less constrained by current experiments and clocks will be able to explore uncharted territory.…”