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 \approx 0.2 , n _ { s } \approx 0.96 with e-folds number N \approx 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 \Lambda \sim ( 10 ^ { 14 } \text { 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 .