Domain wall constraints on two-Higgs-doublet models with Z2 symmetry

The two-Higgs-doublet model (2HDM) with spontaneously broken Z2 symmetry predicts a production of domain walls at the electroweak scale. We derive cosmological constraints on model parameters for both type-I and type-II 2HDMs from the requirement that domain walls do not dominate the Universe by the present day. For type-I 2HDMs, we deduce the lower bound on the key parameter tan β > 105 for a wide range of Higgs-boson masses ∼100 GeV or greater, close to the Standard Model alignment limit. In addition, we perform numerical simulations of the 2HDM with an approximate as well as an exact Z2 symmetry but biased initial conditions. In both cases, we find that domain wall networks are unstable and, hence, do not survive at late times. The domain walls experience an exponential suppression of scaling in these models, which can help ameliorate the stringent constraints found in the case of an exact discrete symmetry. For a 2HDM with softly broken Z2 symmetry, we relate the size of this exponential suppression to the soft-breaking bilinear parameter m12, allowing limits to be placed on this parameter of order μeV, such that domain wall domination can be avoided. In particular, for type-II 2HDMs, we obtain a corresponding lower limit on the CP-odd phase θ generated by QCD instantons, θ ≳ 1011/(sin β cos β), which is in some tension with the upper limit of θ ≲ 1011–1010, as derived from the nonobservation of a nonzero neutron electric dipole moment. For a Z2-symmetric 2HDM with biased initial conditions, we are able to relate the size of the exponential suppression to a biasing parameter ε so as to avoid domain wall domination.