PTA Frequency Band Individual Gravitational Wave Sources and Dark Energy Detection Based on Cosmological Simulation

Abstract: 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 ($\tau_H = 0.1/5/10$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 \leq 5$Gyr) could constrain the dark energy equation-of-state (EoS) parameter $w$ to $\Delta w \sim 0.023$--$0.048$, where the constraints only exhibit weak dependence on $\tau_H$ within $0.1$--$5$Gyr. If only $10\%$ of GW sources have detectable electromagnetic counterparts, constraints weaken to $\Delta w = 0.075$ ($\tau_H = 0.1$Gyr) and $\Delta w = 0.162$ ($\tau_H = 5$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 $\Delta w$ precision by $\sim 40\%$.