(ed.). Gravitational waves (IOP, 2001)(422s).

Gravitational waves, theory and experiment (an overview) 7treats stochastic gravitational waves. As the authors explain, the stochasticgravitational-wave background (SGWB) is a random background of gravitationalwaves without any specific sharp frequency component that might giveinformation about the very early stages of our universe. It is important to note thatrelic cosmological gravitational waves emitted near the big bang might provideunique information on our universe at a very early stage. Indeed, as regards thecosmic microwave background radiation, electromagnetic waves decoupled a few10 5 years after the big bang, whereas relic cosmological gravitational waves, theauthors explain, might come from times as early as a few 10 −44 s. The authorsdiscuss that, in order to increase the chances of detecting a stochastic backgroundof gravitational waves, the correlation of the outputs between two, or more,detectors would be convenient. Thus, after discussing three different detectors:laser interferometers, cylindrical bars and spherical antennae, the authors presentvarious possibilities of correlation, between two laser interferometers (VIRGO,LIGOs, GEO-600 and TAMA-300), and between a laser interferometer and acylindrical bar (AURIGA, NAUTILUS, EXPLORER) or a spherical antenna; theyalso discuss correlation between more than two detectors.In the second part of this paper they discuss sources of the background ofstochastic gravitational waves: topological defects in the form of points, linesor surfaces, called monopoles, cosmic strings and domain walls. In particular,they discuss cosmic strings and hybrid defects; inflationary cosmological models;string cosmology; and first-order phase transitions which occurred in the earlystage of the expansion of the universe, for example in GUT-symmetry breakingand electroweak-symmetry breaking. Finally, they discuss astrophysical sourcesof stochastic gravitational waves. The conclusion is that the frequency domainof cosmological and astrophysical sources of stochastic gravitational wavesmight be very different and thus, the authors conclude, the astrophysicalbackgrounds might not mask the detection of a relic cosmological gravitationalwavebackground at the frequencies of the laser interferometers on Earth.The contribution by Nicolai and Nagar deals with the symmetry propertiesof Einstein’s vacuum field equations when the theory is reduced from four to twodimensions, namely in the presence of two independent spacelike commutingKilling vectors. Under these conditions, and using the vierbein formalism, theauthors show that one can use a Kaluza–Klein ansatz to rewrite the Einstein–Hilbert Lagrangian in the form of two different two-dimensionally reducedLagrangians named the Ehlers and Matzner–Misner ones, respectively, after thepeople who first introduced them. Each of these two Lagrangians representstwo-dimensional reduced gravity in the conformal gauge as given by a part ofpure two-dimensional gravity, characterized by a conformal factor and a dilatonfield plus a ‘matter part’ given by two suitable bosonic fields. In either case, thematter part has a structure of a nonlinear sigma model with an SL(2,R)/SO(2)symmetry. These two different nonlinear symmetries can be combined into aunified infinite-dimensional symmetry group of the theory, called the Gerochgroup, whose Lie algebra is an affine Kac–Moody algebra, and whose action on