Prospective constraints on dark energy from nanohertz individual gravitational wave sources

Nanohertz gravitational waves (GWs) from supermassive binary black holes (SMBBHs), detectable via pulsar timing arrays (PTAs), offer a novel avenue to constrain dark energy. Based on cosmological simulations and semi-analytic galaxy formation models, this study explores the detectability of individual nanohertz SMBBH sources using next-generation PTAs and their potential for constraining dark energy under an optimistic scenario considering only the presence of white noise. By constructing light-cone SMBBH populations across hardening timescales (${\tau }_H=0.1\mathrm{/}5\mathrm{/}10$Gyr) and computing signal-to-noise ratios (SNR), we find advanced PTAs can resolve ${10}^2$–${10}^3$ sources with SNR $>8$ (primarily at $z<1$ with chirp masses of ${10}^8$–${10}^{10}{M}_{\odot }$). If electromagnetic counterparts can be identified, optimal configurations (${\sigma }_t=50$ns, $N_p=1000$, $T_{\text{obs}}=30$yr with${\tau }_H\le 5$Gyr) could constrain the dark energy equation-of-state (EoS) parameter $w$ to $\mathrm{\Delta }w\sim 0.023$–$0.048$, where the constraints only exhibit weak dependence on ${\tau }_H$ within $0.1$–$5$Gyr. If only $10\mathrm{\%}$ of GW sources have detectable electromagnetic counterparts, constraints weaken to $\mathrm{\Delta }w=0.075$ (${\tau }_H=0.1$Gyr) and $\mathrm{\Delta }w=0.162$ (${\tau }_H=5$Gyr) under the most optimal parameter configuration. What’s more, conservative PTAs ($N_p=500$, ${\sigma }_t=100$–$200$ns) with additional $30$-year data accumulation could double resolvable source counts and improve $\mathrm{\Delta }w$ precision by $\sim 40\mathrm{\%}$.