Asymptotically Safe Higgs Inflation

We construct a new inflation model in which the standard model Higgs boson couples minimally to gravity and acts as the inflaton. Our construction of Higgs inflation incorporates the standard model with Einstein gravity which exhibits asymptotic safety in the ultraviolet region. The slow roll condition is satisfied at large field value due to the asymptotically safe behavior of Higgs self-coupling at high energies. We find that this minimal construction is highly predictive, and is consistent with both cosmological observations and collider experiments.Comment: 16pp, to match JCAP Final Version, only minor refinements, references adde

Extending Higgs Inflation with TeV Scale New Physics

Higgs inflation is among the most economical and predictive inflation models, although the original Higgs inflation requires tuning the Higgs or top mass away from its current experimental value by more than $2\sigma$ deviations, and generally gives a negligible tensor-to-scalar ratio $r \sim 10^{-3}$ (if away from the vicinity of critical point). In this work, we construct a minimal extension of Higgs inflation, by adding only two new weak-singlet particles at TeV scale, a vector-quark $T$ and a real scalar $S$. The presence of singlets $(T, S)$ significantly impact the renormalization group running of the Higgs boson self-coupling. With this, our model provides a wider range of the tensor-to-scalar ratio $r = O(0.1 - 10^{-3})$, consistent with the favored $r$ values by either BICEP2 or Planck data, while keeping the successful prediction of the spectral index $n_s \simeq 0.96$. It further allows the Higgs and top masses to fully fit the collider measurements. We also discuss implications for searching the predicted TeV-scale vector-quark $T$ and scalar $S$ at the LHC and future high energy pp colliders.Comment: 20pp, to match JCAP Final Versio

Spontaneous Spacetime Reduction and Unitary Weak Boson Scattering at the LHC

Theories of quantum gravity predict spacetime dimensions to become reduced at high energies, a striking phenomenon known as spontaneous dimensional reduction (SDR). We construct an effective electroweak theory based on the standard model (SM) and incorporate the TeV-scale SDR, which exhibits good high energy behavior and ensures the unitarity of weak gauge boson scattering. This also provides a natural solution to the hierarchy problem in the presence of scalar Higgs boson. We demonstrate that this model predicts unitary longitudinal weak boson scattering, and can be discriminated from the conventional 4d SM by the WW scattering experiments at the CERN LHC.Comment: Phys. Lett. B (in Press). arXiv admin note: text overlap with arXiv:1112.102

Higgs Gravitational Interaction, Weak Boson Scattering, and Higgs Inflation in Jordan and Einstein Frames

We study gravitational interaction of Higgs boson through the unique dimension-4 operator $\xi H^\dag H R$, with $H$ the Higgs doublet and $R$ the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling $\xi$ on weak gauge boson scattering in both Jordan and Einstein frames. We explicitly establish the longitudinal-Goldstone boson equivalence theorem with nonzero $\xi$ coupling in both frames, and analyze the unitarity constraints. We study the $\xi$-induced weak boson scattering cross sections at O(1-30)TeV scales, and propose to probe the Higgs-gravity coupling via weak boson scattering experiments at the LHC(14TeV) and the next generation pp colliders (50-100TeV). We further extend our study to Higgs inflation, and quantitatively derive the perturbative unitarity bounds via coupled channel analysis, under large field background at the inflation scale. We analyze the unitarity constraints on the parameter space in both the conventional Higgs inflation and the improved models in light of the recent BICEP2 data.Comment: 40pp, JCAP Final Version. Use jcappub.sty, only minor rewordings, references adde

Gravitational Interaction of Higgs Boson and Weak Boson Scattering

With the LHC discovery of a 125 GeV Higgs-like boson, we study gravitational interaction of the Higgs boson via the unique dimension-4 operator involving Higgs doublet and scalar curvature, $\,\xi H^\dag H R\,$, with nonminimal coupling $\,\xi\,$. This Higgs portal term can be transformed away in Einstein frame and induces gauge-invariant effective interactions in the Higgs sector. We study the weak boson scattering in Einstein frame, and explicitly demonstrate the longitudinal-Goldstone boson equivalence theorem in the presence of $\,\xi\,$ coupling. With these, we derive unitarity bound on the Higgs gravitational coupling $\,\xi\,$ in Einstein frame, which is stronger than that inferred from the current LHC Higgs measurements. We further study $\xi$-dependent weak boson scattering cross sections at TeV scale, and propose a new LHC probe of the Higgs-gravity coupling $\,\xi\,$ via weak boson scattering experiments.Comment: 7pp, Phys.Rev.D Published Version. All results + conclusions un-changed. Only minor rewording to clarify the Importance of this wor

Higgs Inflation, Reheating and Gravitino Production in No-Scale Supersymmetric GUTs

We extend our previous study of supersymmetric Higgs inflation in the context of no-scale supergravity and grand unification, to include models based on the flipped SU(5) and the Pati-Salam group. Like the previous SU(5) GUT model, these yield a class of inflation models whose inflation predictions interpolate between those of the quadratic chaotic inflation and Starobinsky-like inflation, while avoiding tension with proton decay limits. We further analyse the reheating process in these models, and derive the number of e-folds, which is independent of the reheating temperature. We derive the corresponding predictions for the scalar tilt and the tensor-to-scalar ratio in cosmic microwave background perturbations, as well as discussing the gravitino production following inflation.Comment: JCAP Final Version. 23pp, 3 Figs. Only minor refinements, references adde

Supereulerian graphs and the Petersen graph, II

In this note, we verify two conjectures of Catlin in [J. Graph Theory 13 (1989) 465 - 483] for graphs with at most 11 vertices. These are used to prove the following theorem which improves prior results in [10] and [13]: Let G be a 3-edge-connected simple graph with order n. If n is large and if for every edge 11.v E E(G), d(u) + d(v) 2 % - 2, then either G has a spanning eulerian subgraph or G can be contracted to the Petersen graph