Resonant Loop Interferometers for High-Frequency Gravitational Waves

Gravitational waves at kilohertz and higher frequencies offer a unique probe of the early Universe at temperatures well beyond the reach of the cosmic microwave background, corresponding to energy scales $\gtrsim {10}^9$GeV. Existing detector concepts fall many orders of magnitude short of the big-bang nucleosynthesis (BBN) bound on the stochastic background in this regime. We propose a new interferometric architecture based on closed optical loops, in which the gravitational-wave-induced phase shift accumulates coherently over many traversals. This produces sharp, narrowband resonances whose predictable comb structure provides a distinct experimental signature. For a folded loop with parameters compatible with the Einstein Telescope infrastructure, and finesse values of order 500, we project sensitivity that approaches and even surpasses the BBN bound up to tens of kilohertz after one year of integration. Such loop interferometers thus open a realistic and distinctive path toward exploring high-frequency stochastic gravitational-wave backgrounds.