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 detect nearly the entire annual binary neutron star merger population up to a redshift of 0.5, localizing over 10,000 events within $10\ \mathrm{deg}^2$, including $\sim 150$ 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. Notably, replacing the 20 km CE detector with LIGO-India operating in A$^\sharp$ sensitivity (I$^\sharp$) retains comparable performance, achieving a similar number of detections and localization of over 9,000 events within $10\ \mathrm{deg}^2$ and $\sim 90$ events within $0.1\ \mathrm{deg}^2$. This configuration detects over $\sim 6,000$ events with luminosity distance uncertainties under 10%, including $\sim 50$ events with under 1%. Both networks are capable of detecting $\mathcal{O}(100)$ events up to 10 minutes before merger, with localization areas $\leq 10\ \mathrm{deg}^2$. While I$^\sharp$'s $5\times $ longer baseline with CE, compared to a second CE in the United States, achieves excellent localization and early warning capabilities, its shorter arms and narrower sensitivity band would limit its effectiveness for other science goals, e.g. detecting population III binary black hole mergers at $z \gtrsim 10$, neutron star mergers at $z \sim 2$, or constraining cosmological parameters.