Crunching away the hierarchy or the cosmological constant problem

I present a novel approach to hierarchies related to crunching of regions of space-time. First we use this approach to solve the Higgs hierarchy problem by coupling the SM Higgs to a dilaton of a spontaneously broken CFT, where the dilaton potential will be in a long-lived metastable minimum if the Higgs VEV is below ~ 1 TeV, otherwise it will quickly settle to a minimum with a large negative CC leading to a big crunch. The experimental prediction of this model is a light (<10 GeV) dilaton with very weak coupling to SM particles via its mixing with the Higgs. Along a similar direction we can also provide a new paradigm for the CC problem: regions of space with a large CC will be very short lived, and only those with a small CC survive to date. This requires a super-cooled phase transition which can again be implemented by assuming the presence of a hidden CFT sector, leading to a prediction of additional relativistic degrees of freedom observable at the next round of CMB measurements.