Space missions to detect the cosmic gravitational-wave background

TL;DR

This work develops a coordinate-free formalism to quantify the response of cross-correlated space-based interferometers to a stochastic cosmic gravitational-wave background (CGB). It derives the single-arm Doppler and full interferometer responses, applies them to the LISA geometry, and defines the overlap reduction function $\gamma(f)$ that governs cross-detector sensitivity. By optimizing the cross-correlation filter, the study shows that two LISA-like detectors can achieve dramatic SNR gains over a single detector, enabling potential detection of scale-invariant CGBs with amplitudes as low as $\Omega_{\rm gw} h_0^2 \sim 10^{-14}$ under favorable conditions, and down to even smaller values with larger baselines and lower acceleration noise. The paper further discusses mission designs (LISA I/II/III) and the frequency ranges where astrophysical foregrounds dominate, outlining practical paths to detect or constrain the CGB in ultra-low-frequency bands ($\lesssim 1\,\mu$Hz).

Abstract

It is thought that a stochastic background of gravitational waves was produced during the formation of the universe. A great deal could be learned by measuring this Cosmic Gravitational-wave Background (CGB), but detecting the CGB presents a significant technological challenge. The signal strength is expected to be extremely weak, and there will be competition from unresolved astrophysical foregrounds such as white dwarf binaries. Our goal is to identify the most promising approach to detect the CGB. We study the sensitivities that can be reached using both individual, and cross-correlated pairs of space based interferometers. Our main result is a general, coordinate free formalism for calculating the detector response that applies to arbitrary detector configurations. We use this general formalism to identify some promising designs for a GrAvitational Background Interferometer (GABI) mission. Our conclusion is that detecting the CGB is not out of reach.

Figures (7)

• Figure 1: Possible sources of a stochastic gravitational wave background plotted against the sensitivity curve for the LISA mission.
• Figure 2: The coordinate system used to evaluate LISA's transfer function.
• Figure 3: The magnitudes of the detector response functions $F^+(\widehat{\Omega},f)$ and $F^\times(\widehat{\Omega},f)$ in the low frequency limit.
• Figure 4: The effective noise floor for the LISA mission. The solid line was obtained numerically while the dashed line is our analytic approximation.
• Figure 5: The hexagonal cross correlation pattern.