Prospective constraints on dark energy from nanohertz individual gravitational wave sources

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 ($τ_H = 0.1/5/10$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 ($σ_t = 50$ns, $N_p = 1000$, $T_{\text{obs}} = 30$yr with$ τ_H \leq 5$Gyr) could constrain the dark energy equation-of-state (EoS) parameter $w$ to $Δw \sim 0.023$--$0.048$, where the constraints only exhibit weak dependence on $τ_H$ within $0.1$--$5$Gyr. If only $10\%$ of GW sources have detectable electromagnetic counterparts, constraints weaken to $Δw = 0.075$ ($τ_H = 0.1$Gyr) and $Δw = 0.162$ ($τ_H = 5$Gyr) under the most optimal parameter configuration. What's more, conservative PTAs ($N_p = 500$, $σ_t = 100$--$200$ns) with additional $30$-year data accumulation could double resolvable source counts and improve $Δw$ precision by $\sim 40\%$.

Figures (8)

• Figure 1: The all-sky map of angular distribution for our light-cone GW sources around redshift $z=0.09$ in the $\tau_H=0.1$Gyr case.
• Figure 2: The all-sky map of angular distribution for MSPs, where colors are used to indicate the distances from these pulsars to Earth, and the red star symbol marks the direction of the Galactic Center.
• Figure 3: Scatter plots showing the distributions of SNR versus redshift (top row), mass ratio of binary black holes (middle row), and chirp mass (bottom row) for all bright sources with SNR $>$ 8 in the most optimal case with hardening timescale $\tau_H=0.1\rm Gyr$. The left column displays results for different total observation duration (with other parameters set as $N_p$=1000, $\sigma_t$=100 ns); The middle column displays results under different timing error level (with other parameters set as $N_p=1000$, $T_{\rm obs}=20\rm yr$); The right column displays results for different numbers of pulsars (with other parameters set as $\sigma_t$=100 ns, $T_{\rm obs}=20\rm yr$).
• Figure 4: The number of realizations versus the number count of resolvable GW sources for different PTA parameter configurations in the $\tau_{H}=0.1$ Gyr case. The upper and lower panels represent the results for $N_p=500$ and $1000$, respectively, while the left, middle, and right panels correspond to results for $\sigma_t=200\rm ns$, $100\rm ns$ and $50\rm ns$ respectively.
• Figure 5: The number of realizations versus the number count of resolvable GW sources for different PTA parameter configurations in the $\tau_{H}=5$ Gyr case. The upper and lower panels represent the results for $N_p=500$ and $1000$, respectively, while the left, middle, and right panels correspond to results for $\sigma_t=200\rm ns$, $100\rm ns$ and $50\rm ns$ respectively.