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, [Formula: see text] for [Formula: see text]. In the typical inflationary scenario, we predict [Formula: see text] and [Formula: see text] which are consistent with Planck data released in 2015 quite well. Subtracting the contribution of thermal dust measured by Planck, BICEP2 data implies [Formula: see text] which is the tightest bound on the tensor-to-scalar ratio from current experiments.
Circular polarization of gravitational waves from early-Universe helical turbulence
