The observed value of the Higgs boson mass indicates that the Higgs potential becomes small and flat at the scale around ${10}^{17}\text{ }\text{ }\mathrm{GeV}$. Having this fact in mind, we reconsider the Higgs inflation scenario proposed by Bezrukov and Shaposhnikov. It turns out that the nonminimal coupling $$\xi${}$ of the Higgs squared to the Ricci scalar can be smaller than 10. For example, $$\xi${}=7$ corresponds to the tensor-to-scalar ratio $r$\simeq${}0.2$, which is consistent with the recent observation by BICEP2.

The observed Higgs mass $M_H=125.9\pm 0.4\mathrm{GeV}$ leads to the criticality of the standard model, that is, the Higgs potential becomes flat around the scale $10^{17–18}\mathrm{GeV}$ for the top mass 171.3 GeV. Earlier we proposed a Higgs inflation scenario in which this criticality plays a crucial role. In this paper, we investigate the detailed cosmological predictions of this scenario in light of the latest Planck and BICEP2 results. We also consider the Higgs portal scalar dark matter model, and compute the Higgs one-loop effective potential with the two-loop renormalization group improvement. We find a constraint on the coupling between the Higgs boson and dark matter which depends on the inflationary parameters.

We compute one- and two-loop quadratic divergent contributions to the bare Higgs mass in terms of the bare couplings in the Standard Model. We approximate the bare couplings, defined at the ultraviolet cutoff scale, by the $\overline{\mathrm{MS}}$ ones at the same scale, which are evaluated by the two-loop renormalization group equations for the Higgs mass around 126 GeV in the Standard Model. We obtain the cutoff scale dependence of the bare Higgs mass, and examine where it becomes zero. We find that when we take the current central value for the top quark pole mass, 173 GeV, the bare Higgs mass vanishes if the cutoff is about ${10}^{23}\text{ }\text{ }\mathrm{GeV}$. With a $1.3\text{ }\text{ }$\sigma${}$ smaller mass, 170 GeV, the scale can be of the order of the Planck scale.

We analyze time evolution of a spherically symmetric collapsing matter from a point of view that black holes evaporate by nature. We first consider a spherical thin shell that falls in the metric of an evaporating Schwarzschild black hole of which the radius $a(t)$ decreases in time. The important point is that the shell can never reach $a(t)$ but it approaches $a(t)-a(t)\frac{\mathrm{d}a(t)}{\mathrm{d}t}$. This situation holds at any radius because the motion of a shell in a spherically symmetric system is not affected by the outside. In this way, we find that the collapsing matter evaporates without forming a horizon. Nevertheless, a Hawking-like radiation is created in the metric, and the object looks the same as a conventional black hole from the outside. We then discuss how the information of the matter is recovered. We also consider a black hole that is adiabatically grown in the heat bath and obtain the interior metric. We show that it is the self-consistent solution of $G_{\mu \nu }=8\pi G⟨T_{\mu \nu }⟩$ and that the four-dimensional Weyl anomaly induces the radiation and a strong angular pressure. Finally, we analyze the internal structures of the charged and the slowly rotating black holes.

We consider the Higgs portal Z ₂ scalar model as the minimal extension of the Standard Model (SM) to incorporate the dark matter. We analyze this model by using the two-loop renormalization group equations. We find that the dark matter mass is bounded to be lighter than 1000 GeV within the framework that we have proposed earlier, where the Higgs inflation occurs above the SM cutoff Λ, thanks to the fact that the Higgs potential becomes much smaller than its typical value in the SM: V ≪ Λ⁴. We can further fix the dark matter mass to be 400 GeV < m _DM < 470 GeV if we impose that the cutoff is at the string scale Λ ~ 10¹⁷ GeV and that the Higgs potential becomes flat around Λ, as is required by the multiple point principle or by the Higgs inflation at the critical point. This prediction is testable by the dark matter detection experiments in the near future. In this framework, the dark matter and top quark masses are strongly correlated, which is also testable.

We analyze the time evolution of a spherically-symmetric collapsing matter from the point of view that black holes evaporate by nature. We consider conformal matters and solve the semi-classical Einstein equation $G_{\mu \nu }=8\pi G\langle T_{\mu \nu }\rangle$ by using the four-dimensional Weyl anomaly with a large c coefficient. Here, $\langle T_{\mu \nu }\rangle$ contains the contribution from both the collapsing matter and Hawking radiation. The solution indicates that the collapsing matter forms a dense object and evaporates without horizon or singularity, and it has a surface, but looks like an ordinary black hole from the outside. Any object we recognize as a black hole should be such an object.