Dark Matter, Dark Radiation and Gravitational Waves from Mirror Higgs
  Parity
  An exact parity replicates the Standard Model giving a Mirror Standard Model,
SM $\leftrightarrow$ SM$'$. This "Higgs Parity" and the mirror electroweak
symmetry are spontaneously broken by the mirror Higgs, $\left\langle
H'\right\rangle = v' \gg \left\langle H\right\rangle$, yielding the Standard
Model Higgs as a Pseudo-Nambu-Goldstone Boson of an approximate $SU(4)$
symmetry, with a quartic coupling $\lambda_{SM}(v') \sim 10^{-3}$. Mirror
electromagnetism is unbroken and dark matter is composed of $e'$ and
$\bar{e}'$. Direct detection may be possible via the kinetic mixing portal, and
in unified theories this rate is correlated with the proton decay rate. With a
high reheat temperature after inflation, the $e'$ dark matter abundance is
determined by freeze-out followed by dilution from decays of mirror neutrinos,
$\nu' \rightarrow \ell H$. Remarkably, this requires $v' \sim (10^8 - 10^{10})$
GeV, consistent with the Higgs mass, and a Standard Model neutrino mass of
$(10^{-2} - 10^{-1})$ eV, consistent with observed neutrino masses. The mirror
QCD sector exhibits a first order phase transition producing gravitational
waves that may be detected by future observations. Mirror glueballs decay to
mirror photons giving dark radiation with $\Delta N_{\rm eff} \sim 0.03 - 0.4$.
With a low reheat temperature after inflation, the $e'$ dark matter abundance
is determined by freeze-in from the SM sector by either the Higgs or kinetic
mixing portal.
