8.2 Origin of a random background of gravitational waves

8.2.1 Gravitational waves from the Big Bang

Gravitational waves have traveled almost unimpeded through the universe since they were generated. The cosmic microwave background [74] is a picture of the universe at a time 3 × 105 yrs after the Big Bang, and studies of nucleosynthesis [349] (how the primordial hydrogen, helium, deuterium, and lithium were created) reveal conditions in the universe a few minutes after the Big Bang. Gravitational waves, on the other hand, were produced at times earlier than 10–24 s after the Big Bang. Observing this background would undoubtedly be one of the most important measurements that gravitational wave astronomy could make. It would provide a test of inflation, and it would have the potential to give information about the fundamental interactions of physics at energies far higher than we can reach with accelerators.

The most well-defined predictions about the energy in the cosmological gravitational wave background come from inflationary models. Inflation is an attractive scenario for the early universe because, among other things, it provides a natural mechanism for producing the initial density perturbations that evolved into galaxies and galaxy clusters as the universe expands. These perturbations start out as quantum fluctuations in the (hypothetical) scalar inflaton field that is responsible for the inflationary expansion of the universe. The fluctuations are parametrically amplified by the expansion [18426430Jump To The Next Citation Point] and lead to fluctuations in the density of normal matter after inflation ends.

Several strands of evidence – among them the statistical distribution of density perturbations seen in the cosmic microwave background (most recently by WMAP [346]), the present distribution of galaxies [229], and numerical simulations of structure formation in the early universe [287] – are fully consistent with the now-standard model of a universe dominated by dark energy and whose matter density is dominated by some kind of cold (i.e., massive) dark matter particles [353] with density perturbations consistent with those that inflation could have produced.

The scalar inflaton fluctuations are accompanied by tensor quantum fluctuations in the gravitational field that similarly get amplified by inflation and form a random background [2930]. Different models of inflation make different predictions about the relative strength of the scalar and tensor components.

Although inflation is in excellent agreement with observation, other mechanisms in the early universe may have led to the additional production of gravitational waves. Defects that arise from symmetry breaking as the presumed early unified interactions separate from one another can lead to cosmic strings [379], which can produce both a continuous observable gravitational wave background [104] and characteristic isolated bursts of gravitational waves [141142143]. String theory [95101Jump To The Next Citation Point] and brane theory [194250] may also provide mechanisms for generating observable radiation.

The various models usually predict significantly different spectra for background radiation. Standard inflationary models predict that the spectrum of Ω gw should be nearly flat, independent of frequency, but variants exist that allow a spectrum that rises with frequency (positive spectral index) or falls. Symmetry-breaking and brane model cosmologies can make very different predictions, even leading to narrow spectral features. It is, therefore, important to measure the spectrum at as many frequencies as possible. Limits on power at one frequency (such as at the very low-frequency end in the cosmic microwave background) do not necessarily predict the power at other frequencies (such as at ground-based frequencies, a factor 1020 times higher).

It is even possible that there will be a feature in the spectrum in the observing band of ground-based or space-based detectors. In standard cosmologies, the radiation observable by LISA (1 mHz) had a wavelength comparable to the (then) horizon size at around the time when the temperature of the universe was equal to the electroweak symmetry-breaking energy. If electroweak symmetry breaking led to a first-order phase transition, where density fluctuations occurred on the length scale of the typical symmetry domain size, then it is likely that these density fluctuations produced gravitational waves with wavelengths of the size of the horizon, which would be in the LISA band today [255]. Detection of this radiation would have deep implications for fundamental physics.

The other expected phase transition is the GUTs (Grand Unified Theory) transition, whose energy might have been 1013 times higher. Any gravitational radiation from this transition today would then be at a frequency 1013 times that from the electroweak transition, i.e., at centimeter wavelengths. This is one motivation for building microwave-based table-top detectors aimed at high frequencies [127]. For this radiation to be observable by standard interferometers, the GUTs transition would have to have an energy 107 times smaller than expected, i.e., around 109 GeV. We shall have to wait for observations at these frequencies to tell us if it is there!

In addressing the possibility of new physics, observation of gravitational waves in the cosmic microwave background would play a unique role. These waves originated long after nucleosynthesis, at energies where physics is presumably well understood. They would, therefore, normalize the amount of power in the initial tensor perturbations. Then observations at higher frequencies can use this normalization to measure the excess energy due to any exotic effects due to string theory, phase transitions, or other unknown physics [185101].

Pulsar timing arrays (see Section 8.1.3) will also be used to search for a CGWB at frequencies of a few nanoHertz. As for the microwave background, the physics of the universe when gravitational waves at these frequencies originated is well understood, so they could be used to normalize the spectrum. If the power at pulsar frequencies and that in the microwave background are not consistent, then this could indicate something about the conditions in the universe before inflation began.

The predicted spectrum from inflation, strings, and symmetry breakings is highly nonthermal. Any thermal radiation produced in the Big Bang (for example, if, hypothetically, there was some kind of equipartition between gravitational degrees of freedom and other fields in the initial data at the singularity, whatever that might mean!) would have been redshifted away to unobservability by the subsequent inflationary expansion. If inflation did not in fact occur, then this radiation today would have a temperature only a little below that of the cosmological microwave background. So far no instrument has been proposed that would be sensitive to this radiation, but its detection would presumably be inconsistent with inflation.

8.2.2 Astrophysical sources of a stochastic background

After galaxy formation, it is possible that many systems arose that have been radiating gravitational waves in the bands observable by pulsar timing, LISA, and ground-based detectors. There are likely to be strong extra-galactic backgrounds in the LISA band from compact binary systems, which would limit searches for a CGWB [328] by LISA, even if the sensitivity were better. At lower frequencies, even down to pulsar timing frequencies, black hole binaries may make the strongest background, while at frequencies above the LISA band (i.e., above 0.1 Hz) the universe should be relatively free of serious backgrounds [158368].

In the LISA band our galaxy is a strong source of backgrounds [192]. This presents a serious confusion noise in searching for other sources at frequencies below 1 mHz. It should be possible to distinguish this from a CGWB by its intrinsic anisotropy [369].

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