How much primordial tensor mode is allowed?
Moumita Aich, Yin-Zhe Ma, Wei-Ming Dai, Jun‐Qing Xia
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 number of relativistic degrees of freedom ${N}_{\mathrm{eff}}$ with the amplitude and shape of the primordial tensor power spectrum, and use the cosmic microwave background temperature and polarization data from Planck and the BICEP2/KECK Array and the primordial deuterium measurements from damped Lyman-$\ensuremath{\alpha}$ systems to constrain this model. We find that with the extra relation $\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}(r,{n}_{\mathrm{t}})$, the tensor-to-scalar ratio $r$ is constrained to be $r<0.07$ ($3\ensuremath{\sigma}$ C.L.) and the tilt of the tensor power spectrum is ${n}_{\mathrm{t}}=\ensuremath{-}0.01\ifmmode\pm\else\textpm\fi{}0.31$ ($1\ensuremath{\sigma}$ C.L.) for $Planck+\mathrm{BICEP}2+\mathrm{KECK}+[\mathrm{D}/\mathrm{H}]$ 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 ${N}_{\mathrm{eff}}=3.122\ifmmode\pm\else\textpm\fi{}0.171$ excludes the possibility of a fourth neutrino species at more than $5\ensuremath{\sigma}$ C.L.