Exploring the Equation of State of the Early Universe: Insights from BBN, CMB, and PTA Observations

Abstract

Strong evidence for a gravitational-wave background (GWB) has been reported in the nano-Hertz band. Interpreting the origin of this background to be scalar-induced gravitational waves (SIGWs), we explore the equation of state (EoS) of the early universe by performing Bayes parameter inferences across the big-bang nucleosynthesis (BBN), cosmic microwave background (CMB), and pulsar timing array (PTA) joint observations for the first time. Assuming a monochromatic power spectrum for primordial curvature perturbations, we obtain the spectral amplitude \(A\sim10^{-3}-10^{-1}\) and spectral peak frequency \(f_\ast\sim10^{-7}-10^{-6}\) Hz. We find that the radiation domination with EoS \(w=1/3\) is compatible with the current observational data, the kination domination with EoS \(w=1\) is not forbidden, while the early matter domination with EoS \(w=0\) is excluded at more than \(2\sigma\) confidence level. These results can be tested with future observations.