Huang, QG (reprint author), Chinese Acad Sci, State Key Lab Theoret Phys, Inst Theoret Phys, Beijing 100190, Peoples R China.
Gravitational waves can escape from the big bang and can be taken as a probe to the physics, in particular the inflation, in the early universe. Planck scale is a fundamental scale for quantum theory of gravity. Requiring the excursion distance of inflaton in the field space during inflation yields an upper bound on the tensor-to-scalar ratio. For example, r < 7 x 10(-4) for n(s) = 0.9645. In the typical inflationary scenario, we predict 1 -2/N < n(s) < 1 and -2/N-2 < alpha(s) < 0 which are consistent with Planck data released in 2015 quite well. Subtracting the contribution of thermal dust measured by Planck, BICEP2 data implies r less than or similar to 0.08 which is the tightest bound on the tensor-to-scalar ratio from current experiments.