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

230 Sources of SGWBwhich is a suitable ansatz for the metric describing an evolving homogeneousisotropic universe. The cosmological field equations derived from the low-energypart of (13.30) have the symmetry (in four dimensions)R(t) → 1R(−t) ,φ(t) → φ(−t) − 6ln[R(−t)]which relates ordinary FRW cosmology characterized by H ≡ Ṙ/R > 0, Ḣ < 0,constant φ (where a dot means a derivative with respect to t) att > 0, with aninflationary one with H > 0, Ḣ > 0 and ˙φ > 0att < 0. This symmetrymay suggest that the universe started its evolution from the state of perturbativevacuum, i.e. empty, cold, flat and decoupled with increasing Hubble parameterand eventually emerged in the standard cosmology at t > 0 with decreasing H and‘frozen’ dilaton. The dual cosmology is called pre-big bang (PBB) phase and itdoes not need a beginning time as H → 0 and φ →−∞for t →−∞. However,the low-energy equations of motion do not smoothly interpolate between thesetwo phases. Instead they lead to singularities, in the past for the FRW phase(as ordinary cosmology) and in the future for the PBB phase; in both cases att = 0 where big bang should be placed. However, the approximations on whichthe validity of equation (13.30) relies, break down whenever H ∼ O(λ s −1)or φ ∼ 0. The corrections indicated in equation (13.30) may prevent reachingthe singularity, allowing a smooth transition to standard hot big bang and FRWcosmology. Actually there are indications (see, e.g., [50–54]) that a regularizationmechanism can be really provided by taking into account of quantum and stringyeffects on the evolution of the system. The big bang should then be identified withthe epoch of maximum but not infinite curvature which should be followed by apost-big bang evolution, by which we mean a standard evolution with = 1, asit has been achieved by the long period of PBB inflation. The above describedscenario is displayed in figure 13.5.Nevertheless in the strong coupling regime physics is really new and theperturbative approach proposed by equation (13.30) is no more valid. One shouldresort to a new picture, with an effective action written in terms of the newlight modes appropriate to the strong coupling regime [55]. Anyway, admittingthat a regularization is still possible makes this picture noteworthy from boththe theoretical and the phenomenological point of view. From the theoreticalside it addresses issues left open by standard inflationary models such as theinitial singularity and the theoretical origin of the field driving inflation; fromthe phenomenological side in the next subsection the production of gravitationalwaves (studied in [56, 57]) will be analysed.13.3.1 The modelThe solution of the equations of motion derived from equation (13.30) whichpresents the initial conditions typical of PBB phase are (for time-dependent only