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

String cosmology 231HPre-big bangPost-big bang0.0Figure 13.5. Qualitative behaviour of H in the suggested cosmological model. Brokencurves indicate the lowest order solution singular at t = 0. At around t = 0 a regularevolution interpolating between the two phases is displayed.0.0tfields):R(η) =− 1H s η s( η − (1 − α)ηsαη s) −α, (13.32)andφ(η) = φ s − γ ln η − (1 − α)η s,η swhere η is the conformal time (see section 13.2) ranging between −∞ and η s < 0,α = ( √ 3 − 1)/2, and γ = √ 3.At a value η = η s the curvature becomes of order of the string scale and thelowest order effective action does not give any more a good description of physics:we enter a ‘full stringy’ regime. One expects that higher order corrections to theeffective action tame the growth of the curvature, and both H and dφ/dt stayapproximatively constant. In terms of conformal time this meansR(η) =− 1H s η , φ(η) = φ s − 2β ln η η s, (13.33)where β is a free parameter which measures the growth of the dilaton in thisphase, which lasts for η s