Effective Field Theories (EFTs) are a model-independent framework which can be used to classify the low-energy effects of heavy, new physics on experimental results which deviate from the Standard Model prediction. It seems increasingly likely that new physics signatures at colliders, for the near future at least, will show up as smaller scale coupling modifications rather than distinct resonances. For this reason, the Standard Model Effective Field Theory (SMEFT), where the Higgs doublet transforms linearly under electroweak symmetry, has gained recent popularity. However, the SMEFT is not as general an EFT as the Higgs EFT (HEFT), where the Higgs doublet transforms non-linearly. The universe, as always, is reluctant to reveal its secrets: is it SMEFT or HEFT\SMEFT (i.e. theories in HEFT but not SMEFT)? Particle colliders will certainly shed some light on this dichotomy, yet they can only probe near our vacuum.
We turn instead to cosmology. First to non-perturbative dynamics, which generically depend on extended field configurations away from the vacuum. For example, the Sphaleron energy is given by field configurations which will be modified in quotient theories. Secondly to the gravitational waves that may have been produced in an early universe phase transition from a false vacuum. Again, this transition would be sensitive to extended field configurations, which in turn could provide us with a new approach from which to probe the SMEFT or HEFT\SMEFT dichotomy, and the nature of electroweak symmetry breaking.