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

Open problems and phenomenological consequences 295of a long inflationary phase requires fine tuning. Originally raised in [24],this problem was recently reproposed as a fundamental difficulty of the prebigbang scenario [25] (see [23, 26–28]).• The second concerns the transition from the pre- to the post-big bang phase,which is expected to occur in the high curvature and strong coupling regime.There is a quantum cosmology approach, based on the scattering of theWheeler–De Witt wavefunction in minisuperspace [7], but the problemseems to require, in general, the introduction of higher derivative (α ′ ) andquantum loop corrections [21,29] in the string effective action (see [15,16]).• The third problem concerns the final matching to the standard Friedman–Robertson–Walker phase, with a transition from the dilaton-dominated tothe radiation-dominated regime, and all the associated problems of dilatonoscillations, reheating, preheating, particle production, entropy production[30], and so on.All these problems are under active investigation, and further work iscertainly needed for a final answer. However, even assuming that all the problemswill be solved in a satisfactory way, we are left eventually with a further question,the third one listed in the introduction, which is the basic question (in ouropinion). Are there phenomenological consequences that can discriminate stringcosmology from the other inflationary scenarios? and, in particular, are suchconsequences observable (at least in principle)?The answer is positive. There are many phenomenological differences, evenif all the differences seem to have the same ‘common denominator’, i.e. the factthat the quantum fluctuations of the background fields are amplified in differentmodels with different spectra. The spectrum, in particular, tends to follow thebehaviour of the curvature scale during the phase of inflation. In the standardscenario the curvature is constant or decreasing, so that the spectrum tends to beflat, or decreasing with frequency. In string cosmology the curvature is growing,and the spectrum tends to grow with frequency.In the following sections we will discuss in detail this effect for thecase of tensor metric perturbations. Here we would like to note that thephenomenological consequences of the pre-big bang scenario can be classifiedinto three different types, depending on the possibility of their observation: typeI effects, referring to observations to be performed in a not so far future (20–30 years?); type II effects, referring to observations to be performed in a nearfuture (a few years); type III effects, referring to observations already (in part)performed. To conclude this very quick presentation of the pre-big bang scenario,let me give one example for each type of phenomenological effect.• Type I: the production of a relic graviton background that, in the frequencyrange of conventional detectors (∼10 2 –10 3 Hz), is much higher (by 8–9orders of magnitude) than the background expected in conventional inflation[8, 31–33]. The sensitivity of the presently operating gravitational antennaeis not enough to detect it, however, and we have to wait for the advanced,