Inflation and Higgs

We briefly review several Higgs inflation models and discuss their cosmological implications. We first classify the inflation models according to the predicted value of the tensor-to-scalar ratio: (i) $r = {\cal O}(0.01-0.1)$, (ii) $r = {\cal O}(10^{-3})$, and (iii) $r \ll 10^{-3}$. For each case we study (i) the Higgs inflation with a running kinetic term, (ii) the Higgs inflation with a non-minimal coupling to gravity, and (iii) the $B-L$ Higgs inflation. In the last case we introduce supersymmetry to suppress the Coleman-Weinberg corrections for successful inflation, and derive the upper bound on the SUSY breaking scale. Interestingly, the SUSY $B-L$ Higgs inflation requires the SUSY breaking scale of order ${\cal O}(100)$\,TeV to explain the observed spectral index. We briefly discuss a topological Higgs inflation which explains the origin of the standard model near-criticality. We also mention the possibility of Higgs domain walls and the gravitational waves emitted by the collapsing domain walls.