Towards a realistic solution of the cosmological constant fine-tuning problem by Higgs inflation

Why is the cosmological constant Λ observed today so much smaller than the Planck scale, and why is the Universe accelerating at present? This is the so-called cosmological constant fine-tuning problem. In this paper, we find that this problem may be solved with the help of Higgs inflation by simply assuming a variable cosmological "constant" during the inflationary epoch. Meanwhile, it could predict a large tensor-to-scalar ratio r ≈0.20 and a large running of the spectral index n_s^'≈-0.028 with a red-tilt spectrum n_s≈0.96 , as well as a big enough number of e -folds N ≈40 , requiring that we solve the problems in big bang cosmology with the help of Λ .