Is cosmological constant needed in Higgs inflation?

The detection of B-mode shows a very powerful constraint to theoretical inflation models through the measurement of the tensor-to-scalar ratio r. Higgs boson is the most likely candidate of the inflaton field. But usually, Higgs inflation models predict a small value of r  , which is not quite consistent with the recent results from BICEP2. In this paper, we explored whether a cosmological constant energy component is needed to improve the situation. And we found the answer is yes. For the so-called Higgs chaotic inflation model with a quadratic potential, it predicts r≈0.2r≈0.2, ns≈0.96ns≈0.96 with e-folds number N≈56N≈56, which is large enough to overcome the problems such as the horizon problem in the Big Bang cosmology. The required energy scale of the cosmological constant is roughly Λ∼(1014 GeV)2Λ∼(1014 GeV)2, which means a mechanism is still needed to solve the fine-tuning problem in the later time evolution of the universe, e.g. by introducing some dark energy component.