  The cosmology of the Twin Higgs requires the breaking of the $\mathbb{Z}_2$
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
$\mathbb{Z}_2$ breaking. We first present a simple toy model that can realize
baryogenesis without explicit $\mathbb{Z}_2$ breaking or reaching temperatures
that would lead to domain walls. The model can also either solve the
$N_{\text{eff}}$ 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.
