The stochastic gravity-wave background: sources and detection

TL;DR

This work provides a rigorous framework for searching for a stochastic gravitational-wave background using cross-correlation between geographically separated detectors. It defines the spectral energy density Ω_gw(f), outlines the assumed statistical properties (isotropy, stationarity, Gaussianity), and derives the optimal filtering approach together with the overlap reduction function γ(f) that accounts for detector geometry. The paper surveys current observational bounds from CMB isotropy, pulsar timing, and BBN, and reviews cosmological sources—inflation, cosmic strings, and first-order phase transitions—detailing their predicted spectra and detectability with LIGO/VIRGO and future missions. Its main contribution is a concrete methodology for estimating the minimum detectable Ω_gw and a comparative analysis of likely signatures from early-universe processes, highlighting the potential for ground- and space-based detectors to probe fundamental physics from the earliest moments of the cosmos.

Abstract

A world-wide effort is now underway to build gravitational wave detectors based on highly-sensitive laser interferometers. When data from detectors at different sites is properly combined, it will permit highly-sensitive searches for a stochastic background of relic gravitational radiation. These lectures (from the Les Houches School in October 1995) review the current status of this program, and discuss the methods by which data from different detectors can be used to make measurements of, or place limits on, a stochastic background. They also review possible cosmological sources and their potential detectability.

Figures (18)

• Figure 1: The solid curve is the fractional energy density $\Omega_{\rm em}(f)$ contained in the $2.73$ K electromagnetic background radiation (with $h_{100}$ set to unity). The dashed curve shows the corresponding quantity for a $0.9$ K blackbody. If the gravitational perturbations had been in equilibrium with the matter fields, this is the expected spectrum of the gravitational wave stochastic background. Both axes are $\rm log_{10}$.
• Figure 2: A conformal diagram showing a spatially-flat Friedman-Robertson-Walker cosmological model. The past light cone of a present-day observer (Here, Now) intersects a surface at $t=10^{-22}$ seconds in a large 2-sphere, of which two points (a,b) are shown. The future light cone of the initial singularity intersects the same surface in a much smaller 2-sphere, of which two points (a,c) are also shown. The number of independent, uncorrelated horizon volumes $N_{\rm horizon}$ which contribute to the gravitational radiation arriving at a detector today is given by the ratio of the areas of the larger 2-sphere to the smaller one.
• Figure 3: This graph shows the two lengths, as functions of cosmological time (both axes are ${\rm log}_{10}$). Today, we are at the far right of the graph, $t \approx 10^{17}$ seconds after the big bang. The solid curve shows the physical wavelength of a wave that LIGO or VIRGO might detect, at $\approx 100 \> \rm Hz$. Today this wavelength is about $3 \times 10^8$ cm; in the past this wavelength shrinks because of redshifting, in proportion to the cosmological scale factor, first as $t^{2/3}$ when the universe is matter dominated, then as $t^{1/2}$ when the universe is radiation dominated. The dotted curve shows the characteristic spatial size (and age) of the universe, the Hubble length, which today is $\approx 10^{28}$ cm. This function grows $\propto t$. The intersection of these two curves determines the time at which the primordial production of gravitons in the LIGO/VIRGO band took place.
• Figure 4: Shown is a the surface of the earth $15^\circ < \rm latitude < 75^\circ$, and $-130^\circ < \rm longitude < 20^\circ$, including the LIGO detectors in Hanford, WA (L1) and Livingston, LA (L2) and the locations of the VIRGO detector (V) in Pisa, Italy and the GEO-600 (G) detector in Hannover, Germany. The perpendicular arms of the LIGO detectors are also illustrated (though not to scale). A plane gravitational wave passing by the earth is indicated by successive minima (troughs), zeros, and maxima (peaks) of the wave. As this wave passes by the pair of LIGO detectors, it excites the detectors in coincidence at the moment shown, because both detectors are driven negative by the wave. During the time when the zero is between L1 and L2, the two detectors respond in anti-coincidence. Provided that the wavelength $\lambda$ of the wave is larger than about twice the separation distance (2998 Km) between the detectors, on the average they are driven in coincidence more of the time than in anti-coincidence.
• Figure 5: The overlap reduction function $\gamma(f)$ for the two LIGO detector sites. (The horizontal axis of the left-hand graph is linear, while that of the right-hand graph is $\rm log_{10}$.) The overlap reduction function shows how the correlation of the detector pair to an unpolarized stochastic background falls off with frequency. The overlap reduction function has its first zero at 64 Hz, as explained earlier. It falls off rapidly at higher frequencies.