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

Inflation 223Hubble radius and when the M ¯M pairs get connected by strings the hybrid systemcollapse in less than one Hubble time by dissipating energy into friction with thecosmological fluid.For our purposes, the most interesting scenario is when the monopoles areformed during the inflation but are not completely inflated away. The strings areformed later with a length scale ξ that is much smaller than the average monopoleseparation d. In the course of the evolution ξ grows like t and eventually becomescomparable to d, so that at some time t m we are left with M ¯M pairs connected bystrings. If the strings are formed during inflation, soon after the monopoles, theydo not go through a period of relativistic evolution and no gravitational radiation isproduced prior to t m . In contrast, if the strings are formed in the post-inflationaryepoch, they can have a period of relativistic evolution and a nearly flat stochasticbackground identical to that for walls bounded by strings is produced before t m .At t > t m , the M ¯M pairs oscillate and gradually convert their energy ingravitational radiation. This process has been studied in detail in [38] for thesimplest case of a straight string connecting the monopoles. It was found that thespectral density of the radiation emitted by this simple configuration verify theboundh 2 0 gw º 2 × 10 −8 (13.19)in the frequency range of VIRGO.13.2 InflationIt is well known that many of the shortcomings of the standard cosmologicalmodel (such as isotropy of the CMBR, structure formation, flatness and monopoleproblems) can be successfully faced in the framework of the so-called inflationarymodels (see [39, 40] for a review).The basic idea shared by almost all the various models [41–44] of inflationis that in early times the universe was dominated by the vacuum energy ofsome scalar field, which provided an exponential growth of the scale factorof the universe; then, as a result of a phase transition (maybe associated witha spontaneous symmetry breaking), the scalar field was captured by the trueminimum of its potential, made some oscillations and finally settled down in it.The energy previously stored in the false vacuum was converted into the decayproducts of the scalar field, produced mainly during the oscillatory stage: thisprocess is responsible for the reheating of the universe, thus providing the usual‘hot’ initial conditions for the beginning of the radiation-dominated era.Despite the fact that a complete and satisfying model of inflation is not yet athand, the ‘inflationary paradigm’, i.e. the idea of a primordial stage of acceleratedexpansion, is widely accepted and considered as a necessary ingredient of everycosmological model. Moreover, an inflationary stage provides a very interestingmechanism of amplification of perturbations (see [47]) that, as well as beingimportant for what concerns the problem of the structures formation, generates