Feng, CJ (reprint author), Shanghai Normal Univ, Shanghai United Ctr Astrophys, 100 Guilin Rd, Shanghai 200234, Peoples R China.
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 approximate to 0.20 and a large running of the spectral index n(s)' approximate to -0.028 with a red-tilt spectrum n(s) approximate to 0.96, as well as a big enough number of e-folds N approximate to 40, requiring that we solve the problems in big bang cosmology with the help of Lambda.