Beyond Standard Model:Higgs-gravitational Interactions In Particle Physics And Cosmology

In this thesis we study the theory and observable effects of Higgs gravitational interaction, focusing on electroweak symmetry breaking and cosmic inflation. We explore possible quantum gravitational effects in electroweak symmetry breaking, and new mechanism of Higgs-driven inflation in early universe, in order to deepen our understanding toward electroweak breaking beyond the Standard Model as well as quantum gravity.We firstly study a novel quantum gravitational effect known as spontaneous dimensional reduction(SDR). We construct a model-independent effective field theory of SDR,and apply it to the electroweak scale. We use this effective theory to illustrate the improved unitarity of partial wave amplitude of longitudinal boson scattering due to SDR. We also find new signals for longitudinal boson scattering from SDR and quantum-gravity-induced Higgs anomalous coupling. Then, we study the non-minimal coupling between the Higgs field and the scalar curvature of the spacetime. We explicitly verify the Goldstone boson equivalence theorem, and justify the equivalence between Jordan and Einstein frame in computing scattering amplitudes of longitudinal bosons. We derive a unitarity bound for the non-minimal coupling, and study its signal at LHC and future colliders.In the second part of the thesis, we introduce the Higgs Inflation model in which the Standard Model Higgs field is identified as inflaton, and study its unitarity problem. We get quantitative unitarity bound on this theory by computing Goldstone amplitude with large inflaton background, and justify the unitarity of Higgs inflation. We also discuss the effect of quantum correction to Higgs inflation, and the related problem of Higgs instability, as well as the necessity of new physics beyond the Standard Model.Then we introduce three scenarios of Higgs inflation with new physics. Firstly, we study the effect of new neutral scalar and vector quark of TeV mass to the Higgs inflation. Then we describe a class of grand unification theories in the framework of no-scale supergravity, and realize Higgs inflation in this type of theory. For this purpose we use supersymmetric SU(5) as an example, and then generalize it to Flipped SU(5) and PatiSalam model. At last, we describe an asymptotically safe Higgs inflation, in which the gravity reaches a non-Gaussian fixed point in high energy, while matter couplings flow to trivial fixed point. This scenario will make Higgs potential flat enough to satisfy slow-roll condition, and to achieve a successful inflation. All these three scenarios can guarantee the stability of Higgs vacuum, and are consistent with collider measurements of Higgs and top quark masses.