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6.3. Gravitational waves from strings

Next generation of gravitational waves instruments yield a good prospect of detecting a stochastic GW background generated in the very early universe. This opens up a brand new window, in some sense comparable to the advent of radio-astronomy to complement the existing (and as we know, limited) optical-astronomy, many years ago now. In fact, if one had to limit oneself to those events accessible through electromagnetic radiation alone, many of the most interesting of these events would remain outside our reach. The CMB provides a snapshot of the universe at about 400,000 years, just as the universe became transparent to electromagnetic radiation. But what about those processes that happened before the photon decoupling `surface'?

Gravitational waves can penetrate through the electromagnetic surface of last scattering thanks to the remarkable transparency of the gravitons and their very weak interactions with ordinary matter. One can then, by detecting this relic background (in `upper case') get information from the earliest possible times, namely the Planck era ~ 10-43 seconds after the Bang.

For radiation emitted at a time te before the time of equal matter and radiation energy densities, i.e., with te < teq ~ 40,000 years, and with a wavelength comparable to the horizon lambda(te) ~ te, the GW frequency today is f ~ zeq-1(teq te)-1/2 where zeq ~ 2.3 × 104 Omega0 h2.

In experiments one measures


with Omegag(f) giving the energy density in gravitational radiation in an octave frequency bin centred on f, and where h is the Hubble parameter in units of 100 km s-1 Mpc-1 and rhoc is the critical density.

We saw above that a network of cosmic strings quickly evolved in a self similar manner with just a few infinite string segments per Hubble volume and Hubble time. To achieve this, the generation of small loops and the subsequent decay of these daughter loops was required. Both local and global oscillating cosmic string loops are then a possible cosmological source of gravitational waves (see Figure 1.22) with local strings producing the strongest signal, as GW emission is their main decay channel (there is also the production of Goldstone bosons in the global case) [Caldwell & Allen, 1992; Battye & Shellard, 1996].

Figure 22

Figure 1.22. A summary of the spectral density versus frequency for various potential sources of a stochastic gravitational wave background. Included in this busy plot are the amplitudes of GW from different types of inflationary scenarios, from a first-order electroweak phase transition, and from both gauge and global cosmic strings, also including the primordial 0.9 K blackbody spectrum of gravitons. [Battye & Shellard, 1996].

Figure 23

Figure 1.23. A series of snapshots from a two interlocked cosmic string loop decay process [courtesy of R. Battye and P. Shellard]. Loops disintegrate through the emission of (mainly gravitational) radiation. However, if endowed with currents, the loops may eventually reach equilibrium configurations (vortons) which will prevent their radiative decay. Such a population of vortons would jeopardize the so far successful standard model, unless it is produced at low enough energies.

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