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

Why is the cosmological constant [Lambda] 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 [asymptotically =] 0.20 and a large running of the spectral index n' sub(s) [asymptotically =] -0.028 with a red-tilt spectrum n sub(s) [asymptotically =] 0.96, as well as a big enough number of e-folds N [asymptotically =] 40, requiring that we solve the problems in big bang cosmology with the help of [Lambda].