In the minimal modified functional measure model, a logarithmic scalar-potential correction can make the electroweak transition strongly first order, and future gravitational-wave observatories could probe the Higgs trilinear coupling at a level competitive with near-future colliders.
Massive graviton from diffeomorphism invariance
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We describe a mechanism in which the graviton acquires a mass from the functional measure without violating the diffeomorphism symmetry nor including St\"uckelberg fields. Since gauge invariance is not violated, the number of degrees of freedom goes as in general relativity. For the same reason, Boulware-Deser ghosts and the vDVZ disconinuity do not show up. The graviton thus becomes massive at the quantum level while avoiding the usual issues of massive gravity.
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Cosmological phase transitions from the functional measure
In the minimal modified functional measure model, a logarithmic scalar-potential correction can make the electroweak transition strongly first order, and future gravitational-wave observatories could probe the Higgs trilinear coupling at a level competitive with near-future colliders.