We present a systematic introduction to the diagrammatic method for practical calculations in inflationary cosmology, based on Schwinger-Keldysh path integral formalism. We show in particular that the diagrammatic rules can be derived directly from a classical Lagrangian even in the presence of derivative couplings. Furthermore, we use a quasi-single-field inflation model as an example to show how this formalism, combined with the trick of mixed propagator, can significantly simplify the calculation of some in-in correlation functions. The resulting bispectrum includes the lighter scalar case (m < 3H/2) that has been previously studied, and the heavier scalar case (m > 3H/2) that has not been explicitly computed for this model. The latter provides a concrete example of quantum primordial standard clocks, in which the clock signals can be observably large. *
We study gravitational interaction of Higgs boson through the unique dimension-4 operator ξH † HR , with H the Higgs doublet and R the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling ξ on weak gauge boson scattering in both Jordan and Einstein frames. We explicitly establish the longitudinal-Goldstone boson equivalence theorem with nonzero ξ coupling in both frames, and analyze the unitarity constraints. We study the ξ-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 (14 TeV) and the next generation pp colliders (50 − 100 TeV). 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.
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