International audienceThis document outlines a set of simplified models for dark matter and its interactions with Standard Model particles. It is intended to summarize the main characteristics that these simplified models have when applied to dark matter searches at the LHC, and to provide a number of useful expressions for reference. The list of models includes both s-channel and t-channel scenarios. For s-channel, spin-0 and spin-1 mediation is discussed, and also realizations where the Higgs particle provides a portal between the dark and visible sectors. The guiding principles underpinning the proposed simplified models are spelled out, and some suggestions for implementation are presented

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A fundamental property of the Standard Model is that the Higgs potential becomes unstable at large values of the Higgs field. For the current central values of the Higgs and top masses, the instability scale is about 10 11 GeV and therefore not accessible by colliders. We show that a possible signature of the Standard Model Higgs instability is the production of gravitational waves sourced by Higgs fluctuations generated during inflation. We fully characterise the two-point correlator of such gravitational waves by computing its amplitude, the frequency at peak, the spectral index, as well as their three-point correlators for various polarisations. We show that, depending on the Higgs and top masses, either LISA or the Einstein Telescope and Advanced-Ligo, could detect such stochastic background of gravitational waves. In this sense, collider and gravitational wave physics can provide fundamental and complementary informations. Since the mechanism described in this paper might also be responsible for the generation of dark matter under the form of primordial black holes, this latter hypothesis may find its confirmation through the detection of gravitational waves. Contents

The idea that primordial black holes (PBHs) can comprise most of the dark matter of the universe has recently reacquired a lot of momentum. Observational constraints, however, rule out this possibility for most of the PBH masses, with a notable exception around 10 −12 M . These light PBHs may be originated when a sizeable comoving curvature perturbation generated during inflation re-enters the horizon during the radiation phase. During such a stage, it is unavoidable that gravitational waves (GWs) are generated. Since their source is quadratic in the curvature perturbations, these GWs are generated fully non-Gaussian. Their frequency today is about the mHz, which is exactly the range where the LISA mission has the maximum of its sensitivity. This is certainly an impressive coincidence. We show that this scenario of PBHs as dark matter can be tested by LISA by measuring the GW two-point correlator. On the other hand, we show that the short observation time (as compared to the age of the universe) and propagation effects of the GWs across the perturbed universe from the production point to the LISA detector suppress the bispectrum to an unobservable level. This suppression is completely general and not specific to our model. arXiv:1810.12224v3 [astro-ph.CO] 30 Jul 2019 1 We briefly comment on the high-mass portion of Fig. 1. The Ultra-Faint Dwarf (UFD) galaxy constraint arises from the fact that PBHs of this mass would cause the dissolution of star clusters observed in UFDs such as Eridanus II [27]; this constraint is strongly weakened in the presence of an intermediate-mass black hole, providing a binding energy that stabilizes the cluster [27,28]. We thank Juan García-Bellido for discussions on this issue. Secondly, we do not show in Fig. 1 the lensing bounds related to the measured luminosities of Supernovae Ia derived in [29,30], which constrain the abundance of PBHs above 1 M . We are not showing also the stronger bounds from CMB arising from disk-accretion [31]. We also omitted the constraints coming from Lyman−α forest observations [32], which overlap with the ones from UFD. Similarly, in the low-mass region, we do not show the constraints from [33] related the production of cosmic rays from evaporating PBHs, given that they overlap with the constraints related to γ−rays produced by the PBHs evaporation.