Planckian Interacting Massive Particles as Dark Matter

The standard model could be self-consistent up to the Planck scale according to the present measurements of the Higgs boson mass and top quark Yukawa coupling. It is therefore possible that new physics is only coupled to the standard model through Planck suppressed higher dimensional operators. In this case the weakly interacting massive particle miracle is a mirage, and instead minimality as dictated by Occam’s razor would indicate that dark matter is related to the Planck scale, where quantum gravity is anyway expected to manifest itself. Assuming within this framework that dark matter is a Planckian interacting massive particle, we show that the most natural mass larger than $0.01M_p$ is already ruled out by the absence of tensor modes in the cosmic microwave background (CMB). This also indicates that we expect tensor modes in the CMB to be observed soon for this type of minimal dark matter model. Finally, we touch upon the Kaluza-Klein graviton mode as a possible realization of this scenario within UV complete models, as well as further potential signatures and peculiar properties of this type of dark matter candidate. This paradigm therefore leads to a subtle connection between quantum gravity, the physics of primordial inflation, and the nature of dark matter.

Figure 1

The value of the Hubble rate at the start of reheating that gives the correct relic abundance, as a function of the mass of the PIDM. The blue curve is for $\gamma =1$, the orange curve is for $\gamma =0.1$, and the green curve is for $\gamma =0.01$. The red region is excluded from the current bound on the tensor-to-scalar ratio, and the purple dashed line is the projected sensitivity for next generation CMB experiments, from Ref. [24]. The dotted lines show the modification when taking also gravitational production into account [12, 13, 14]. The dashed-dotted line marks $m_X=H_i$, and for a scalar PIDM the left-hand side of this line is excluded unless corrections to the PIDM potential are important during inflation. All values are given in units of $M_p$.