The Critical Role of LIGO-India in the Era of Next-Generation Observatories

We examine the role of LIGO-India in facilitating multi-messenger astronomy in the era of next generation observatories. A network with two L-shaped Cosmic Explorer (CE) detectors and one triangular Einstein Telescope (ET) would precisely localize nearly the entire annual binary neutron star merger population up to a redshift of 0.5--over 10,000 events would be localized within $10\ \mathrm{deg}^2$, including approximately 150 events within $0.1\ \mathrm{deg}^2$. Luminosity distance would be measured to within 10% for over 9,000 events and within 1% for $\sim 100$ events. Surprisingly, replacing the 20 km CE detector with LIGO-India operating at A$^\sharp$ sensitivity (I$^\sharp$) yields nearly identical performance. The factor-of-five shorter arms are offset by a fourfold increase in baseline relative to a second CE in the U.S., preserving localization accuracy, with over 9,000 events within $10\ \mathrm{deg}^2$ and $\sim 90$ events within $0.1\ \mathrm{deg}^2$. This configuration detects $\sim 6,000$ events with luminosity distance uncertainties under 10%, including $\sim 50$ events with under 1%. Both networks provide $\mathcal{O}(100)$ early-warning detections up to 10 minutes before merger, with localization areas $\leq 10\ \mathrm{deg}^2$. While I$^\sharp$ enables excellent localization and early warnings, its shorter arms and narrower sensitivity band would limit its reach for other science goals, such as detecting population III binary black hole mergers at $z \gtrsim 10$, neutron star mergers at $z \sim 2$, or constraining cosmological parameters.