Introduction to recycling

All the long baseline interferometers for the detection of gravitational radiation which are presently being studied are based on the construction of a large, Michelson-like interferometer with an armlength of 1 to 4 km, containing some kind of gravito-optic transducer in each arm. In order to improve the shot-noise limited sensitivity, all these interferometers will use high-power lasers, in conjunction with so-called light recycling techniques. The basic idea of recycling was proposed by R. W. P. Drever (1983): it consists in building a resonant optical cavity which contains the interferometer, so that, if the losses are low and if the cavity is kept on resonance with the incoming monochromatic light, there is a power build-up which results in a reduction of the shot noise. This can be realized in different ways, depending on the geometry of the gravito-optic transducer (delay line or Fabry-Perot).

A general theory of recycling interferometers was recently developed and published (Vinet et al, 1988) and the Garching (Schnupp, 1987) and Orsay (Man, 1987) groups have obtained the first experimental verifications of the efficiency of this technique. In this chapter, we first remind the reader of the main ideas and results of the theory, which is fully expressed in Vinet et al. (1988). We then describe today's experimental achievements, and we end up with a short discussion of possible future improvements.

Space, time, and gravitation

GENERAL RELATIVITY is Einstein's theory of gravitation. It is not only a theory of gravity: it is a theory of the structure of space and time, and hence a theory of the dynamics of the universe in its entirety. The theory is a vast edifice of pure geometry, indisputably elegant, and of great mathematical interest.

When general relativity emerged in its definitive form in November 1915, and became more widely known the following year with the publication of Einstein's famous exposé Die Grundlage der allgemeinen Relativitätstheorie in Annalen der Physik, the notions it propounded constituted a unique, revolutionary contribution to the progress of science. The story of its rapid, dramatic confirmation by the bending-of-light measurements associated with the eclipse of 1919 is thrilling part of the scientific history. The theory was quickly accepted as physically correct—but at the same time acquired a reputation for formidable mathematical complexity. So much so that it is said that when an American newspaper reporter asked Sir Arthur Eddington (the celebrated astronomer who had led the successful solar eclipse expedition) whether it was true that only three people in the world really understood general relativity, Eddington swiftly replied, “Ah, yes—but who's the third?”

THE AIM OVER the next two chapters is to construct a solution of Einstein's equations with sources that will provide a model for the large scale features of the universe. First, we must find a reasonable form for the metric and energy-moment urn tensor consistent with the observed symmetries of the universe. Then we shall be led to specific cosmological models by the imposition of the Einstein equations.

We are thinking of the average features of the universe on the scale of tens of millions of light years and we may regard the basic building blocks as clusters of galaxies. The first observational fact about the universe that we must use is that the observed distribution of the clusters of galaxies is isotropic to a high degree. If we assume that our position is in no particular way privileged, we must assume the universe is isotropic about every point, which leads to an assumption of homogeneity.

We must distinguish a preferred class of observers, namely those that actually see the universe as isotropic. Thus our cosmological model admits a preferred time-like vector field ua , tangent to the world lines of the preferred or ‘fundamental’ observers.

WE PROCEED to solve the geodesic equations in the Schwarzschild solution and use the solution to describe the classical tests of general relativity. These are the precession of the perihelion of planetary orbits and the bending of light by the sun, effects that arise from the small differences between orbits in Newtonian gravitation and orbits, i.e. geodesies, in general relativity.