Cosmology of the Twin Higgs without explicit ℤ₂ breaking

The cosmology of the Twin Higgs requires the breaking of the ℤ₂ symmetry, but it is still an open question whether this breaking needs to be explicit. In this paper, we study how the Mirror Twin Higgs could be modified to be compatible with current cosmological constraints without explicit ℤ₂ breaking. We first present a simple toy model that can realize baryogenesis without explicit ℤ₂ breaking or reaching temperatures that would lead to domain walls. The model can also either solve the N_eff problem and bring the abundance of mirror atoms to an allowed level or provide the correct dark matter abundance. We then present another simple model that leads to mirror neutron dark matter and thus acceptable dark matter self-interactions. We also include in appendix a series of results on energy exchange between different sectors that might prove useful for other cosmological problems.