Inflation with Non-minimal Gravitational Couplings and Supergravity

We explore in the supergravity context the possibility that a Higgs scalar may drive inflation via a non-minimal coupling to gravity characterised by a large dimensionless coupling constant. We find that this scenario is not compatible with the MSSM, but that adding a singlet field (NMSSM, or a variant thereof) can very naturally give rise to slow-roll inflation. The inflaton is necessarily contained in the doublet Higgs sector and occurs in the D-flat direction of the two Higgs doublets.Comment: 13 pages, 1 figur

Comment on Higgs Inflation and Naturalness

We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.Comment: 5 pages, 1 figure V3: Journal Versio

On Inflation with Non-minimal Coupling

A simple realization of inflation consists of adding the following operators to the Einstein-Hilbert action: (partial phi)^2, lambda phi^4, and xi phi^2 R, with xi a large non-minimal coupling. Recently there has been much discussion as to whether such theories make sense quantum mechanically and if the inflaton phi can also be the Standard Model Higgs. In this note we answer these questions. Firstly, for a single scalar phi, we show that the quantum field theory is well behaved in the pure gravity and kinetic sectors, since the quantum generated corrections are small. However, the theory likely breaks down at ~ m_pl / xi due to scattering provided by the self-interacting potential lambda phi^4. Secondly, we show that the theory changes for multiple scalars phi with non-minimal coupling xi phi dot phi R, since this introduces qualitatively new interactions which manifestly generate large quantum corrections even in the gravity and kinetic sectors, spoiling the theory for energies > m_pl / xi. Since the Higgs doublet of the Standard Model includes the Higgs boson and 3 Goldstone bosons, it falls into the latter category and therefore its validity is manifestly spoiled. We show that these conclusions hold in both the Jordan and Einstein frames and describe an intuitive analogy in the form of the pion Lagrangian. We also examine the recent claim that curvature-squared inflation models fail quantum mechanically. Our work appears to go beyond the recent discussions.Comment: 14 pages, 2 figures. Version 2: Clarified findings and improved wording. Elaborated important sections and removed an unnecessary section. Added references. Version 3: Updated towards JHEP version. Version 4: Final JHEP versio

Mixing of Active and Sterile Neutrinos

We investigate mixing of neutrinos in the $\nu$MSM (neutrino Minimal Standard Model), which is the MSM extended by three right-handed neutrinos. Especially, we study elements of the mixing matrix $\Theta_{\alpha I}$ between three left-handed neutrinos $\nu_\alpha$ ($\alpha = e,\mu,\tau$) and two sterile neutrinos $N_I$ ($I=2,3$) which are responsible to the seesaw mechanism generating the suppressed masses of active neutrinos as well as the generation of the baryon asymmetry of the universe (BAU). It is shown that $\Theta_{eI}$ can be suppressed by many orders of magnitude compared with $\Theta_{\mu I}$ and $\Theta_{\tau I}$, when the Chooz angle $\theta_{13}$ is large in the normal hierarchy of active neutrino masses. We then discuss the neutrinoless double beta decay in this framework by taking into account the contributions not only from active neutrinos but also from all the three sterile neutrinos. It is shown that $N_2$ and $N_3$ give substantial, destructive contributions when their masses are smaller than a few 100 MeV, and as a results $\Theta_{e I}$ receive no stringent constraint from the current bounds on such decay. Finally, we discuss the impacts of the obtained results on the direct searches of $N_{2,3}$ in meson decays for the case when $N_{2,3}$ are lighter than pion mass. We show that there exists the allowed region for $N_{2,3}$ with such small masses in the normal hierarchy case even if the current bound on the lifetimes of $N_{2,3}$ from the big bang nucleosynthesis is imposed. It is also pointed out that the direct search by using $\pi^+ \to e^+ + N_{2,3}$ and $K^+ \to e^+ + N_{2,3}$ might miss such $N_{2,3}$ since the branching ratios can be extremely small due to the cancellation in $\Theta_{eI}$, but the search by $K^+ \to \mu^+ + N_{2,3}$ can cover the whole allowed region by improving the measurement of the branching ratio by a factor of 5.Comment: 30 pages, 32 figure

Higgs Starobinsky inflation

In this paper we point out that Starobinky inflation could be induced by quantum effects due to a large non-minimal coupling of the Higgs boson to the Ricci scalar. The Higgs Starobinsky mechanism provides a solution to issues attached to large Higgs field values in the early universe which in a metastable universe would not be a viable option. We verify explicitly that these large quantum corrections do not destabilize Starobinsky's potential

Three-loop \beta-functions for top-Yukawa and the Higgs self-interaction in the Standard Model

We analytically compute the dominant contributions to the \beta-functions for the top-Yukawa coupling, the strong coupling and the Higgs self-coupling as well as the anomalous dimensions of the scalar, gluon and quark fields in the unbroken phase of the Standard Model at three-loop level. These are mainly the QCD and top-Yukawa corrections. The contributions from the Higgs self-interaction which are negligible for the running of the top-Yukawa and the strong coupling but important for the running of the Higgs self-coupling are also evaluated.Comment: 22 pages, 7 figures. Few extra citations are added; the plots are improved. Results in computer readable form can be retrieved from http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp12/ttp12-012

The mu problem and sneutrino inflation

We consider sneutrino inflation and post-inflation cosmology in the singlet extension of the MSSM with approximate Peccei-Quinn(PQ) symmetry, assuming that supersymmetry breaking is mediated by gauge interaction. The PQ symmetry is broken by the intermediate-scale VEVs of two flaton fields, which are determined by the interplay between radiative flaton soft masses and higher order terms. Then, from the flaton VEVs, we obtain the correct mu term and the right-handed(RH) neutrino masses for see-saw mechanism. We show that the RH sneutrino with non-minimal gravity coupling drives inflation, thanks to the same flaton coupling giving rise to the RH neutrino mass. After inflation, extra vector-like states, that are responsible for the radiative breaking of the PQ symmetry, results in thermal inflation with the flaton field, solving the gravitino problem caused by high reheating temperature. Our model predicts the spectral index to be n_s\simeq 0.96 due to the additional efoldings from thermal inflation. We show that a right dark matter abundance comes from the gravitino of 100 keV mass and a successful baryogenesis is possible via Affleck-Dine leptogenesis.Comment: 27 pages, no figures, To appear in JHE

Inflation and dark matter in two Higgs doublet models

We consider the Higgs inflation in the extension of the Standard Model with two Higgs doublets coupled to gravity non-minimally. In the presence of an approximate global U(1) symmetry in the Higgs sector, both radial and angular modes of neutral Higgs bosons drive inflation where large non-Gaussianity is possible from appropriate initial conditions on the angular mode. We also discuss the case with single-field inflation for which the U(1) symmetry is broken to a Z_2 subgroup. We show that inflationary constraints, perturbativity and stability conditions restrict the parameter space of the Higgs quartic couplings at low energy in both multi- and single-field cases. Focusing on the inert doublet models where Z_2 symmetry remains unbroken at low energy, we show that the extra neutral Higgs boson can be a dark matter candidate consistent with the inflationary constraints. The doublet dark matter is always heavy in multi-field inflation while it can be light due to the suppression of the co-annihilation in single-field inflation. The implication of the extra quartic couplings on the vacuum stability bound is also discussed in the light of the recent LHC limits on the Higgs mass.Comment: (v1) 28 pages, 8 figures; (v2) 29 pages, a new subsection 3.3 added, references added and typos corrected, to appear in Journal of High Energy Physic