A battle of designs: triangular vs. L-shaped detectors and parity violation in the gravitational-wave background

TL;DR

This work assesses the detectability of a parity-violating gravitational-wave background using third-generation ground-based detector networks centered on one Einstein Telescope and two Cosmic Explorers. It extends the GWB formalism to include the V-mode (circular polarization) and introduces PI sensitivity curves to compare I- and V-mode prospects across multiple ET geometries and network layouts. Through both SNR-based and Bayesian analyses, the authors demonstrate that ET with a 2L design significantly enhances PV sensitivity, while triangular ET configurations perform poorer in the V-mode, even when arm lengths are increased. The results underscore the critical role of global network design in enabling or constraining parity-violating physics in the early Universe and provide actionable guidance for optimizing future detector configurations.

Abstract

We investigate the prospects for detecting a parity-violating gravitational-wave background (GWB) with third-generation ground-based detector networks. We focus on a network consisting of one Einstein Telescope (ET) and two Cosmic Explorer (CE) detectors. In our analysis we vary the ET design, detector orientations, and arm lengths, in order to assess the impact of geometry and scale on detection capabilities. We demonstrate that networks with an L-shaped ET design have stronger parity violation constraining power than networks with a triangular ET design, particularly seen when studying ET designs on their own.

Figures (6)

• Figure 1: PI sensitivity curves for $I$-mode (solid lines) and $V$-mode (dotted and dashed lines), shown for the seven different detector third-generation network configurations for an observing time of one year and $\rho=4$. The $V$-mode curves correspond to $|\Pi| = 1$ (dotted) and $|\Pi| = 0.1$ (dashed).
• Figure 2: SNRs for $I$-mode (solid lines) and $V$-mode (dashed lines) for the seven third-generation detector network configurations, assuming a flat ($\alpha=0$) power-law GWB.
• Figure 3: SNR and log Bayes detection prospects for $I$- and $V$-modes in a flat GWB in the $\Delta_{10}$(PY)$_5$ and (SR)$_3$(PY)$_3$ configurations. The green and purple filled regions correspond to $95 \%$ exclusion regions of $\Pi=0$. The gray-shaded region indicates where $\rho_V^{\Delta_{10} \text{(PY)}_5} \leq \rho_V^{95\%,~\rm{crit}} \leq \rho_V^{\text{(SR)}_3 \text{(PY)}_3}$, where $\rho_V^{95\%,~\rm{crit}} = 2.16$ is the approximate $V$-mode SNR where $\Pi=0$ is excluded at 95%. The red star marks the case study discussed in Sec. \ref{['subsec: dataAnalysis_PE']}.
• Figure 4: Posterior distributions from Bayesian inference for parity-violating power-law GWBs, combined over 15 simulated runs for $f_{\rm ref}=25$ Hz. Shown are the (SR)$_3$(PY)$_3$ (purple) and $\Delta_{10}$(PY)$_5$ (green) networks, with dark and light shading indicating $1\sigma$ and $2\sigma$ credible regions. Here: $\Pi = -1$ and $\log_{10} \Omega_{\alpha} = -11.54$ shown in blue.
• Figure 5: PI curves sensitivity curves for I-mode (solid lines) and V-mode (dotted and dashed lines), shown for the 6 different ET configurations, for an observing time of one year and $\rho=4$. The V-mode curves correspond to $|\Pi| = 1$ (dotted) and $|\Pi| = 0.1$ (dashed). We also show PL GWBs with spectral index of $\alpha=0$.