Evidence for a stochastic gravitational wave background in the nHz frequency band is recently reported by four pulsar timing array collaborations NANOGrav, EPTA, CPTA, and PPTA. It can be interpreted by gravitational waves from collapsing domain walls in the early universe. We assume such domain walls arising from the spontaneous breaking of a $Z_2$ symmetry in a scalar field theory, where a tiny $Z_2$-violating potential is required to make domain walls unstable. We propose that this $Z_2$-violating potential is radiatively induced by a feeble Yukawa coupling between the scalar field and a fermion field, which is also responsible for dark matter production via the freeze-in mechanism. Combining the pulsar timing array data and the observed dark matter relic density, we find that the model parameters can be narrowed down to small ranges.

We study the collider phenomenology of the electroweak phase transition and electroweak baryogenesis in the framework of the effective field theory. Our study shows that the effective theory using the dimension-6 operators can enforce strong first order phase transition and provide sizable $CP$ violation to realize a successful electroweak baryogenesis. Such dimension-6 operators can induce interesting Higgs phenomenology that can be verified at colliders such as the LHC and the planning CEPC. We then demonstrate that this effective theory can originate from vectorlike quarks and the triplet Higgs.

The AMS-02 Collaboration has just published a high-precision measurement of the cosmic positron fraction ${e}^{+}/({e}^{-}+{e}^{+})$, which rises with energy from $$\sim${}5\text{ }\text{ }\mathrm{GeV}$ to $$\sim${}350\text{ }\text{ }\mathrm{GeV}$. The result indicates the existence of primary electron/positron sources to account for the positron excess. In this work, we investigate the possibility that the nearby mature pulsars with ages of $O({10}^{5})\text{ }\text{ }\mathrm{yr}$ are the primary positron sources. By fitting the data we find that the positrons from a single nearby pulsar, such as Geminga or Monogem, with the spectral index $$\alpha${}$\sim${}2$ can interpret the AMS-02 result. We also investigate the possibility that high-energy positrons are generated by multiple known pulsars in the ATNF catalogue. Such a scenario can also fit the AMS-02 data well. Future precise measurements of fine structures in the positron spectrum would be a support to the pulsar scenario.

The recent reported 750 GeV diphoton excess at the 13 TeV LHC is explained in the framework of effective field theory assuming the diphoton resonance is a scalar (pseudoscalar) particle. It is found that the large production rate and the broad width of this resonance are hard to be simultaneously explained if only visible final states are considered. Therefore an invisible decay channel to dark matter (DM) is strongly favored by the diphoton resonance with a broad width, given a large coupling of the new scalar to DM. We set constraints on the parameter space in this scenario using the results from LHC Run 1, DM relic density, and DM direct and indirect detection experiments. We find that the DM searches can exclude a large portion of the parameter regions accounting for the diphoton excess with a broad width