New Cosmic Microwave Background Constraint to Primordial Gravitational Waves

Abstract

Primordial gravitational waves (GWs) with frequencies $\ensuremath{\gtrsim}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{Hz}$ contribute to the radiation density of the Universe at the time of decoupling of the cosmic microwave background (CMB). This affects the CMB and matter power spectra in a manner identical to massless neutrinos, unless the initial density perturbation for the GWs is nonadiabatic, as may occur if such GWs are produced during inflation or some post-inflation phase transition. In either case, current observations provide a constraint to the GW amplitude that competes with that from big-bang nucleosynthesis (BBN), although it extends to much lower frequencies ($\ensuremath{\sim}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{Hz}$ rather than the $\ensuremath{\sim}{10}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{Hz}$ from BBN): at 95% confidence level, ${\ensuremath{\Omega}}_{\mathrm{gw}}{h}^{2}\ensuremath{\lesssim}8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for homogeneous (i.e., nonadiabatic) initial conditions. Future CMB experiments, like Planck and CMBPol, should allow sensitivities to ${\ensuremath{\Omega}}_{\mathrm{gw}}{h}^{2}\ensuremath{\lesssim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and ${\ensuremath{\Omega}}_{\mathrm{gw}}{h}^{2}\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, respectively.