In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
Quantum gravity fluctua- tions flatten the Planck-scale Higgs potential
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abstract
We investigate asymptotic safety of a toy model of a singlet-scalar extension of the Higgs sector including two real scalar fields under the impact of quantum-gravity fluctuations. Employing functional renormalization group techniques, we search for fixed points of the system which provide a tentative ultraviolet completion of the system. We find that in a particular regime of the gravitational parameter space the canonically marginal and relevant couplings in the scalar sector -- including the mass parameters -- become irrelevant at the ultraviolet fixed point. The infrared potential for the two scalars that can be reached from that fixed point is fully predicted and features no free parameters. In the remainder of the gravitational parameter space, the values of the quartic couplings in our model are predicted. In light of these results, we discuss whether the singlet-scalar could be a dark-matter candidate. Furthermore, we highlight how "classical scale invariance" in the sense of a flat potential of the scalar sector at the Planck scale could arise as a consequence of asymptotic safety.
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Quantum gravity contributions to the beta functions of gauge and Yukawa couplings are derived via the Schwinger proper-time flow equation; their dependence on gauge fixing and regulators is quantified at gravity's interactive fixed point and compared with other schemes.
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
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Towards theory constraints on ultralight dark matter from quantum gravity
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
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Quantum gravity contributions to the gauge and Yukawa couplings in proper time flow
Quantum gravity contributions to the beta functions of gauge and Yukawa couplings are derived via the Schwinger proper-time flow equation; their dependence on gauge fixing and regulators is quantified at gravity's interactive fixed point and compared with other schemes.
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Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.