Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be the Standard Model Higgs boson, the electroweak vacuum would be a metastable state at 98% C.L. In this paper we argue that, during inflation, the electroweak vacuum can actually be very short-lived, contrary to the conclusion that follows from the flat spacetime analysis. Namely, in the case of a pure Higgs potential the electroweak vacuum decays via the Hawking-Moss transition, which has no flat spacetime analogue. As a result, the Higgs vacuum is unstable, unless the rate of inflation is low enough: H inf 10 9 −10 12 GeV. Models of inflation with such a low rate typically predict negligible tensor perturbations in the cosmic microwave background radiation (CMBR). This is also true for models in which the perturbations are produced by a curvaton field. We also find that if the effective curvature of the Higgs potential at a local maximum (which may be induced by inflaton-Higgs interactions) is large enough, then the decay of the electroweak vacuum is dominated by the Coleman-de Luccia transition. The electroweak vacuum is also short-lived in this case, due to a negative effective self-interaction coupling. Based on our analysis of Higgs vacuum stability during inflation, we conclude that the observation of tensor perturbations by the Planck satellite would provide strong indirect evidence for new physics beyond the Standard Model responsible for stabilisation of the electroweak vacuum.

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be a noncommutative extension of the unimodular theory of gravitation. We compute the leading order noncommutative correction to the action and derive the noncommutative correction to the equations of motion of the weak gravitation field.

We investigate a strategy to search for light, nearly degenerate higgsinos within the natural MSSM at the LHC. We demonstrate that the higgsino mass range µ in 100 − 160 GeV, which is preferred by the naturalness, can be probed at 3σ significance through the monojet search at 14 TeV HL-LHC with 3000 fb −1 luminosity. The proposed method can also probe certain region in the parameter space for the lightest neutralino with a high higgsino purity, that cannot be reached by planned direct detection experiments at XENON-1T(2017).