Relaxation of the Composite Higgs Little Hierarchy

We describe a composite Higgs scenario in which a cosmological relaxation mechanism naturally gives rise to a hierarchy between the weak scale and the scale of spontaneous global symmetry breaking. This is achieved through the scanning of sources of explicit global symmetry breaking by a relaxion field during an exponentially long period of inflation in the early universe. We explore this mechanism in detail in a specific composite Higgs scenario with QCD-like dynamics, based on an ultraviolet $SU(N)_{\textrm{TC}}$ 'technicolor' confining gauge theory with three Dirac technifermion flavors. We find that we can successfully generate a hierarchy of scales $\xi \equiv \langle h \rangle^2 / F_\pi^2 \gtrsim 1.2 \times 10^{-4}$ (i.e., compositeness scales $F_\pi \sim 20$ TeV) without tuning. This evades all current electroweak precision bounds on our (custodial violating) model. While directly observing the heavy composite states in this model will be challenging, a future electroweak precision measurement program can probe most of the natural parameter space for the model. We also highlight signatures of more general composite Higgs models in the cosmological relaxation framework, including some implications for flavor and dark matter.