Detecting the Cosmic Gravitational Wave Background with the Big Bang Observer

TL;DR

The paper tackles detecting a Cosmic Gravitational Background in the 0.1–1 Hz band using space-based interferometers by cross-correlating the full set of channels ($A,E,T$) from two co-planar triangular detectors. It derives the GW response and noise transfer for each channel, and computes the overlap reduction function to optimize the cross-correlation signal. Numerical results show that combining all channel pairs yields an orientation-independent, significantly enhanced sensitivity, enabling detection of a scale-invariant background down to $\Omega_{gw}=2.2\times10^{-17}$ for a 5-year mission with the fiducial BBO design. This demonstrates the feasibility of BBO to probe early-Universe cosmology via the CGB and to place stringent constraints on inflationary and related theories.

Abstract

The detection of the Cosmic Microwave Background Radiation (CMB) was one of the most important cosmological discoveries of the last century. With the development of interferometric gravitational wave detectors, we may be in a position to detect the gravitational equivalent of the CMB in this century. The Cosmic Gravitational Background (CGB) is likely to be isotropic and stochastic, making it difficult to distinguish from instrument noise. The contribution from the CGB can be isolated by cross-correlating the signals from two or more independent detectors. Here we extend previous studies that considered the cross-correlation of two Michelson channels by calculating the optimal signal to noise ratio that can be achieved by combining the full set of interferometry variables that are available with a six link triangular interferometer. In contrast to the two channel case, we find that the relative orientation of a pair of coplanar detectors does not affect the signal to noise ratio. We apply our results to the detector design described in the Big Bang Observer (BBO) mission concept study and find that BBO could detect a background with $Ω_{gw} > 2.2 \times 10^{-17}$.

Figures (12)

• Figure 1: $R_{12}(f_{n})/\sin^{2}(f_n)$ for $A_{1} \times A_{2}$
• Figure 2: $R_{12}(f_{n})/\sin^{2}(f_n)$ for $E_{1} \times E_{2}$
• Figure 3: $R_{12}(f_{n})/(1+2\cos(2f_n))^{2}$ for $T_{1} \times T_{2}$
• Figure 4: $R_{12}(f_{n})/((1+2\cos(2 f_n))\sin(f_n))$ for $A_{1} \times T_{2}$ or $T_{1} \times A_{2}$
• Figure 5: $R_{12}(f_{n})/((1+2\cos(2 f_n))\sin(f_n))$ for $E_{1} \times T_{2}$ or $T_{1} \times E_{2}$.