**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 *t*_{e} before the time of
equal matter and radiation energy densities, *i.e.*,
with *t*_{e} < *t*_{eq} ~ 40,000 years, and
with a wavelength comparable to the horizon
(*t*_{e})
~ *t*_{e}, the GW frequency today is *f* ~
*z*_{eq}^{-1}(*t*_{eq}
*t*_{e})^{-1/2} where
*z*_{eq} ~ 2.3 × 10^{4}
_{0}
*h*^{2}.

In experiments one measures

with
_{g}(*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
_{c} 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].