By Yuta Hamada

This thesis makes a speciality of the theoretical starting place of the traditional version legitimate as much as the Planck scale, in accordance with the present experimental proof from the big Hadron Collider. The thesis comprises topics: (1) to open up a brand new window of the Higgs inflation state of affairs, and (2) to discover a brand new technique to the naturalness challenge in particle physics.

In the 1st zone, at the Higgs inflation state of affairs, the writer effectively improves a wide worth challenge on a coupling consistent suitable to the Higgs mass within the normal version, within which the coupling price of the order of 10^{5} anticipated in a traditional state of affairs is diminished to the order of 10. This end result makes the Higgs inflation extra beautiful as the small worth of coupling is ordinary within the context of ultraviolet of entirety resembling string conception. within the moment sector, the writer presents a brand new solution to the naturalness challenge, of why the cosmological consistent and the Higgs mass are tremendous small in comparison with the Planck scale. in line with the newborn universe idea initially proposed through Coleman, the smallness of these amounts is effectively defined with no introducing any extra new debris correct on the TeV power scale.

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If the physics around the Planck scale is strong coupled or the cutoff scale becomes much higher than the Planck scale, we can not neglect the effect of gravitons. 6 Metastability of the Electroweak Vacuum We have seen that our electroweak vacuum is in the critical point, the border between stable and unstable vacuum. However, in practice, even if the electroweak vacuum is unstable, there are no problems provided that the lifetime is sufficiently large compared with the age of the universe. In this case, we call the electroweak vacuum is metastable.

30) √ 2M P . 5 end MP Fig. 3 The slow roll parameters as functions of ϕend . 5 end MP Fig. 4 The inflationary parameters as functions of ϕend . 1 Minimal Higgs Inflation 33 The slow roll parameters as functions of ϕend and N∗ are obtained by substituting Eq. 30) into Eq. 25), which we plot in the Fig. 3. We note that the observed overall amplitude As,obs can be reproduced by taking V1 = 12π 2 As,obs M P4 ϕ∗ MP −2 C + log ϕ∗ MP −3 . 31) We can also calculate the tensor to scalar ratio, running spectral index and so on.

20) Let us consider the action of this solution. From Eq. 2 Coleman’s Argument 47 then the action becomes SE = 1 2 M 2 P √ g E d 4 x(R + 2 ) ⎛ ⎞4 1 2 8π 2 ⎝ 3M P2 ⎠ = MP (−2 ) 2 3 =− 24π 2 M P6 . 22) Next, let us consider the situation that some large S 4 universes are connected by small tube. We call such tube wormhole. The typical size of wormhole is expected to be the Planck scale, and hence we try to sum up wormhole configuration in order to obtain low energy effective action. If one wormhole is inserted, from the view point of large universe, the non-local interaction is induced, so the effect on partition function is given by ⎞ ⎛ Dg ⎝ ci j d 4 xd 4 y g(x) g(y)Oi (x)O j (y)⎠ exp[−SW ] exp[−S E ].