Big Bang Nucleosynthesis Limits and Relic Gravitational Wave Detection Prospects

Big bang nucleosynthesis (BBN) places upper limits on the relativistic energy density in the early universe, which places bounds on the strength of primordial magnetic fields and/or turbulent motions in the early universe and their resulting relic gravitational wave (GW) signals. Previous studies assumed that velocity and magnetic fields are ``frozen-in'' to the primordial plasma and that the ratio between the turbulent source energy density and thermal energy density remain unchanged during the radiation-dominated epoch. We revisit the BBN limits and properly account for the decaying nature of turbulent sources from their generation until BBN. We find that allowed values for the magnetic fields at the moment of generation are not constrained by order of microGauss as was claimed previously based on BBN bounds without accounting for decaying turbulence. This allows larger estimates for the initial magnetic field strength and stronger GW signals than were previously expected. We address the prospects of detecting these GW signals through space-based interferometers (for GWs generated around the electroweak scale) and by pulsar timing arrays and astrometric missions (for GWs generated around the quantum chromodynamics energy scale).