Gravitational waves constrained

Cosmic gravitational waves could provide unprecedented information on the early Universe. The effects that are of interest are small, but experiments are gradually achieving a sensitivity that will test cosmological models.

Gravitational waves are tiny disturbances in space-time. They can be triggered during cataclysmic events involving stars or black holes, and they could even have been generated in the very early Universe, well before any star formed, merely as a consequence of the dynamics and expansion of the Universe. In the latter case, these waves should provide a 'background' signal of gravitational waves coming from all directions in space — if indeed they can be spotted. One particularly sensitive experiment recruited to the search for gravitational waves is LIGO, the Laser Interferometer Gravitational-Wave Observatory. It has just published the results from its fourth bout (S4) of data-taking in The Astrophysical Journal1.

Gravitational waves are not the only known source of cosmic 'noise'. Most famously, the Universe is filled with a background of electromagnetic radiation left behind by the hot Big Bang; it has now cooled to its present temperature of about 2.7 kelvin by the subsequent expansion of the Universe. The discovery of this 'cosmic microwave background' by Arno Penzias and Robert Wilson in 1964 is a milestone in the history of modern cosmology, and its detailed study provides some of our best information on the early Universe. In 1992, NASA's Cosmic Background Explorer (COBE) satellite reported its measurement of the spectrum of the microwave background and found it to have a perfect 'black-body' form with a characteristic temperature that has tiny variations across the sky — the 'seeds' for galaxy formation2. Subsequent experiments, in particular NASA's follow-up WMAP (Wilkinson Microwave Anisotropy Probe) mission, have provided a more detailed picture, and ushered in an epoch of precision cosmology, in which the agreement between experimental data and theoretical models can be at the level of a few per cent.

The discovery of a cosmological background of gravitational radiation would arguably be even more fundamental. Any background of relic particles provides us with a snapshot of the Universe at a very definite time: the time at which these particles decoupled from the primordial plasma. For the photons of the cosmic microwave background, this happened when the Universe was just 270,000 years old. The photons we see today in the cosmic microwave background are a true photograph of the Universe at that age.

The more weakly a particle interacts, the earlier it detaches itself from the primordial plasma. Weakly interacting neutrinos, for instance, decoupled when the Universe was only about a second old. Because the gravitational force is so very small in the realm of elementary particles, the interaction of gravitational waves with the primordial plasma is negligible — they have been propagating freely ever since they were generated. In particular, gravitational waves produced during the Big Bang would carry a genuine picture of the Big Bang itself, providing information that no other messenger can carry.

LIGO, together with its European counterpart VIRGO near Pisa, Italy, is the most ambitious project to date to search for gravitational waves. It consists of three detectors, two on a site in Washington (Fig. 1) and one, 3,000 kilometres away, on a site in Louisiana. The passage of a gravitational wave would cause a tiny delay in the passage of laser beams reflected up and down LIGO's 4-kilometre-long detector arms. Although LIGO has not made a positive detection of gravitational waves, the upper bound on the intensity of a random background is an interesting result in its own right.

Figure 1: Long arms for gravitational waves.


The LIGO site at Hanford, Washington.

The strength of the gravitational-wave background is quantified by its energy density, ρgw. In cosmology, there is a natural unit for energy density, the critical density for 'closing' the Universe, ρc. If the Universe's density is greater than ρc, the force of its own gravity will at some point cause it to begin contracting, ending in a reverse of the Big Bang, the Big Crunch; if, however, it is smaller than this critical density, the Universe's expansion will continue unchecked for ever. It is thus convenient to use the 'normalized' energy density, Ωgw = ρgw/ρc. LIGO's latest upper bound1 for the stochastic gravitational-wave background is Ωgw < 6.5 × 10−5.

This experimental limit is interesting because it represents a sensitivity at which current models of cosmology tell us the detection of gravitational waves is not excluded. Upper bounds on Ωgw can be deduced from various astrophysical and cosmological observations3. In the frequency range accessible to LIGO, the most important limit comes from the production of light elements other than hydrogen in the first few minutes of the Universe, known as Big-Bang nucleosynthesis. The abundance of these light elements is fixed by the balance between the rate of the nuclear reactions that produce them and the expansion rate of the Universe, which dilutes them.

The latter rate is determined, through the equations of general relativity, by the total energy density of the Universe. This consists of the energy density carried by the known elementary particles, plus the energy density carried by any other more exotic form of matter — or indeed by gravitational waves. When only the known elementary particles are included in the computation, theory and observation agree beautifully. The energy density of any other extra particle, and of gravitational waves, at the epoch of nucleosynthesis, is then constrained in order not to spoil this agreement. This puts an upper bound on Ωgw at the level of a few times 10−5, which is comparable to LIGO's new upper bound1.

Certain cosmological models predict values of Ωgw that could be almost as large as is allowed by the nucleosynthesis bound. In particular, a pre-Big-Bang model that includes the low-energy effects of string theory4 predicts a stochastic background of gravitational waves that, for some values of its input parameters, approaches this bound5. Such cosmological models are thus now seeing experimental constraints.

The data from LIGO's S4 run that have now been published1 were taken over a period of one month, between February and March 2005. The duration of the data-taking is a major factor because of the way the stochastic background is extracted by correlating the data of two detectors. This procedure allows the gravitational-wave signal to be extracted from the much greater effect of noise local to the detectors — laser fluctuations, seismic rumblings and so on. This signal-to-noise ratio scales as the square-root of the total observation time.

LIGO is now engaged in its fifth period of data-taking (S5), which will collect one year of coincident data between its detectors, with an improved sensitivity over the S4 data1. The combination of better sensitivity and the longer run is expected to improve the sensitivity to Ωgw by a factor of a further 10−100. In a few years, an upgrade of the experiment, known as Advanced LIGO, should eventually reach sensitivities between 10−8 and 10−9. That should allow us to penetrate deep into a totally unknown region, where the answers to fundamental questions could well be waiting.


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Maggiore, M. Gravitational waves constrained. Nature 447, 651–652 (2007).

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