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The most significant breakthrough in cosmology will be the discovery of background gravitational waves that were produced in the very early universe, during the epoch of rapid expansion known as inflation. We can already look out into space, and hence back in time, to 380,000 years after the bang using the cosmic microwave background radiation. Similarly, by measuring the properties of the neutrino background we can look back to one second after the bang. But gravitational waves are a relic of the universe 10^-35 seconds after the bang.