How much primordial tensor mode is allowed?

TL;DR

This paper constrains the primordial tensor mode amplitude and tilt using CMB and primordial deuterium data, linking them to relativistic degrees of freedom, thus tightening inflation model tests.

Contribution

It introduces a physical model connecting $N_{eff}$ with tensor spectrum parameters and uses combined data to set new tight constraints on primordial gravitational waves.

Findings

Tensor-to-scalar ratio $r<0.07$ at 3$\sigma$

Tensor tilt $n_t=-0.01\pm 0.31$ at 1$\sigma$

Effective neutrino number $N_{eff}=3.122\\pm 0.171$ excludes extra neutrino species

Abstract

The presence of a significant amount of gravitational radiation in the early Universe affects the total energy density and hence the expansion rate in the early epoch. In this work, we develop a physical model to connect the parameter of relativistic degree of freedom $N_\mathrm{eff}$ with the amplitude and shape of primordial tensor power spectrum, and use the CMB temperature and polarization data from {\it Planck} and BICEP2/KECK Array, and the primordial deuterium measurement from damped Lyman-$\alpha$ (DLA) systems to constrain this model. We find that with this extra relation $\Delta N_{\rm eff}(r,n_{\rm t})$, the tensor-to-scalar ratio $r$ is constrained to be $r<0.07$ ($3\sigma$ C.L.) and the tilt of tensor power spectrum is $n_\mathrm{t}=-0.01\pm 0.31$ ($1\sigma$ C.L.) for {\it Planck}+BICEP2+KECK+[D/H] data. This achieves a much tighter constraint on the tensor spectrum and provides a stringent test for cosmic inflation models. In addition, the current constraint on $N_{\rm eff}=3.122 \pm 0.171$ excludes the possibility of fourth neutrino species at more than $5\sigma$ C.L.