We present a UV completion of the twin Higgs idea in the framework of holographic composite Higgs. The SM contribution to the Higgs potential is effectively cut off by the SM-singlet mirror partners at the sigma-model scale f , naturally allowing for mKK beyond the LHC reach. The bulk symmetry is SU (7) × SO(8), broken on the IR brane into SU (7) × SO(7) and on the UV brane into (SU (3) × SU (2) × U (1)) SM × (SU (3) × SU (2) × U (1)) mirror × Z2. The field content on the UV brane is the SM, extended by a sector transforming under the mirror gauge group, with the Z2 exchanging the two sectors. An additional Z2 breaking term is generated holographically to reproduce the Higgs mass and VEV, with a mild O(10%) tuning. This model has no trace at the LHC, but can by probed by precision Higgs measurements at future lepton colliders, and by direct searches for KK excitations at a 100 TeV collider.

We explore the cosmological signatures associated with the twin baryons, electrons, photons and neutrinos in the Mirror Twin Higgs framework. We consider a scenario in which the twin baryons constitute a subcomponent of dark matter, and the contribution of the twin photon and neutrinos to dark radiation is suppressed due to late asymmetric reheating, but remains large enough to be detected in future cosmic microwave background (CMB) experiments. We show that this framework can lead to distinctive signals in large scale structure and in the cosmic microwave background. Baryon acoustic oscillations in the mirror sector prior to recombination lead to a suppression of structure on large scales, and leave a residual oscillatory pattern in the matter power spectrum. This pattern depends sensitively on the relative abundances and ionization energies of both twin hydrogen and helium, and is therefore characteristic of this class of models. Although both mirror photons and neutrinos constitute dark radiation in the early universe, their effects on the CMB are distinct. This is because prior to recombination the twin neutrinos free stream, while the twin photons are prevented from free streaming by scattering off twin electrons. In the Mirror Twin Higgs framework the relative contributions of these two species to the energy density in dark radiation is predicted, leading to testable effects in the CMB. These highly distinctive cosmological signatures may allow this class of models to be discovered, and distinguished from more general dark sectors.

Phase transitions in the early universe can readily create an observable stochastic gravitational wave background. We show that such a background necessarily contains anisotropies analogous to those of the cosmic microwave background (CMB) of photons, and that these too may be within reach of proposed gravitational wave detectors. Correlations within the gravitational wave anisotropies and their cross-correlations with the CMB can provide new insights into the mechanism underlying primordial fluctuations, such as multi-field inflation, as well as reveal the existence of non-standard "hidden sectors" of particle physics in earlier eras.

We present a new solution to the hierarchy problem, where the Higgs mass is at its observed electroweak value because such a patch inflates the most in the early universe. If the Higgs mass depends on a field undergoing quantum fluctuations during inflation, then inflation will fill the universe with the Higgs mass that corresponds to the largest vacuum energy. The hierarchy problem is solved if the maximum vacuum energy occurs for the observed Higgs mass. We demonstrate this notion with a proof-of-principle model containing an axion, a modulus field and the Higgs, and show that inflation can be responsible for the weak scale.