m, N3 would contribute mostly for the lepton asymmetry production. The CP asymmetry generated can be estimated as [302]
3= 3 8πvu2
1 ( ˆm†DmˆD)33
X
i=1,2
Im[( ˆm†DmˆD)2i3]m3
m. (2.57)
Here mˆD represents the rotated Dirac mass matrix in the basis where MR is diagonal. It is found that CP-asymmetry exactly vanishes in this case. We expect this can be cured with the introduction of higher order U(1)R symmetry breaking terms which could be introduced into mD andMR7. Then similar to [303], a non-zero lepton asymmetry through the decay ofN3 can be realized.
2.11 Chapter Summary
We have considered the superpartner of a right-handed neutrino as playing the role of inflaton.
Although a minimal chaotic inflation scenario out of this consideration is a well studied subject, its simplest form is almost outside the 2σregion of recentns−rplot by PLANCK 2015. We have shown in this work, that a mere coupling with the SQCD sector responsible for supersymmetry breaking can be considered as a deformation to the minimal version of the chaotic inflation.
Such a deformation results in a successful entry of the chaotic inflation into the latest ns−r plot. Apart from this, the construction also ensures that a remnant supersymmetry breaking is realized at the end of inflation. The globalU(1)Rsymmetry plays important role in constructing the superpotential for both the RH neutrino as well as SQCD sector. We have shown that the shift-symmetry breaking terms in the set up can be accommodated in an elegant way by introducing spurions. Their introduction, although ad hoc, can not only explain the size of the symmetry breaking but also provide a prescription for operators involving the RH neutrino superfields (responsible for inflation) in the superpotential. With the help of the R-symmetry and the discrete symmetries introduced, we are able to show that light neutrino masses and mixing resulted from the set-up can accommodate the recent available data nicely, predicting an inverted hierarchy for light neutrinos. However there still exists a scope for further study in terms of leptogenesis through the R-symmetry breaking terms.
7We have already mentioned about this possibility of inclusion of such (small) term in the previous section, that can correct the ∆m212 and the lepton mixing angles.
Chapter 3
EW vacuum stability and chaotic Inflation
3.1 Introduction
In the previous chapter we have studied the dynamics of successful chaotic inflation model in supersymmetric framework, where scalar partner of a superfield serve the role of inflaton. Here, in this chapter (based on [304]) we will study non-supersymmetric version of chaotic inflation and how the vacuum stability problem gets affected in presence of the inflation. To accommodate chaotic inflation scenario in a non-supersymmetric framework, one has to extend the SM by an additional scalar field (φ). However as stated in Sec. 1.3.1, the minimal form of chaotic inflation [52] with quadratic potential (Vφ = 12m2φ2) is disfavored by the Planck observations [39]. We have already explored one possible direction in Chapter 2 to save the model from being ruled out. There also exist several other elegant proposals [233, 265, 266, 283, 305–307]. The main idea is to flatten the chaotic inflationary potential dynamically to certain extent so that it can predict correct values of spectral index (ns) and scalar to tensor ratio (r). One particular approach [283] seems interesting in this context where involvement of a second SM singlet scalar field χ (apart from the one, φ, responsible for chaotic inflation) is assumed. The effect of this additional scalar (χ) is to modify the quadratic potential Vφ to some extent.
On the other hand, the chaotic inflation (specifically large scale inflation models) model is also not favored in view of the uncertainty over the stability of EW vacuum. The fluctuations of the Higgs field during inflation might turn dangerous [203, 205, 208, 209, 308] for metastable Higgs vacuum. This is already mentioned in beginning of Sec. 1.3.4.1. However if the effective
62 Chapter 3. EW vacuum stability and chaotic Inflation mass of the Higgs boson can be made sufficiently large during inflation (meffh > HInf), the Higgs field will naturally evolve to origin and the problem can be evaded. This large effective mass term can be generated through Higgs-inflaton interaction as suggested in [309] and the dangerous effect on Higgs vacuum stability during inflation could be avoided. Once the inflation is over, this field can then fall in the EW minimum as this minimum is close to the origin.
In view of the stability of EW vacuum issue, here (based on [304]) we investigate the possibility of using the extra scalar field (χ) of the inflation system (which modifies the chaotic inflation) to take part in resolving the Higgs vacuum stability problem both during and after inflation. During inflation, the Higgs field receives a large Hubble induced mass through its coupling with theχ field, the effect of which is to stabilize the Higgs field at origin and thereby getting rid of any kind of fluctuation during inflation. This ensures that even if the Higgs quartic coupling becomes negative at some scale ΛI (called the instability scale), the Higgs field does not move into region beyond ΛI during inflation. After inflation, the effective Hubble induced mass of the Higgs field decreases. So during the oscillatory phase of the inflaton field and afterwards, this can pose a threat as now the Higgs field can take values beyond ΛI and rolls towards the unstable part of the Higgs potential [207, 310]. This instability issue can be avoided if the Higgs quartic coupling remains positive until a very large scale, e.g. at least upto the inflation scale. It is shown in [58, 59, 311–313] that involvement of a scalar field can indeed modify the stability condition of electroweak vacuum in the SM provided this singlet field acquires a large vacuum expectation value and couples with the SM Higgs at tree level. In our scenario, the χ field of the inflaton system may get a large vacuum expectation value which turns out to be unconstrained from inflationary point of view. Its coupling with the SM Higgs can induce a tree level shift in λh through the threshold correction at a scale below which this scalar would be integrated out. Hence the involvement of a second scalar in the inflaton system turns out to be effective not only in keeping the chaotic inflation in the right ballpark of the existing data from Planck 2015, but also resolves the SM vacuum instability problem by keeping the Higgs quartic coupling positive upto very high scale (even upto MP).
Previously, connecting the inflaton and the Higgs sector to solve the vacuum stability prob- lem has been extensively studied in [314]. They have considered hilltop and quartic inflations where inflaton itself plays the role of this singlet as at the end of inflation, the inflaton field gets a large vev. Below its mass scale the inflaton can be integrated out and the higgs quartic coupling gets a shift. The energy scale where this threshold effect occurs is therefore fixed by the inflaton mass m. Our approach however differs from [314]. Instead of hilltop or quartic inflation, here we employ the chaotic inflation with potential Vφ = m2φ2/2 where φ is the in- flaton field. Following [283] we introduce another scalar field χ, the coupling of which with φ
3.2. Inflation Model 63