Paper detail

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.