Graceful exit via polymerization of pre-big-bang cosmology

We consider a phenomenological modification of the pre-big-bang scenario using ideas from the resolution of curvature singularities in loop quantum cosmology. We show that nonperturbative loop modifications to the dynamics, arising from the underlying polymer representation, can resolve the graceful exit problem. The curvature and the dilaton energy stay finite at all times, in both the string and Einstein frames. In the string frame, the dilaton tends to a constant value at late times after the bounce.

Figure 1

The scale factor $a(t)$ in the Einstein frame: dashed curves are the standard singular PBB solutions; the solid curve is the nonsingular solution after polymer LQC modifications. (We set $M_P=1=\beta$ in all the plots.)

Figure 2

The dilaton $\varphi (t)$ for the standard PBB (dashed) and the LQC polymerized (solid) models.

Figure 3

The Hubble rate $H(t)$ for standard PBB (black, dashed) and LQC polymerized (black, solid) models, and the dilaton velocity $\dot{\varphi }(t)$ in standard (grey, dashed) and polymerized (grey, solid) models.

Figure 4

The Ricci curvature $R(t)$ for LQC polymerized (solid) and standard PBB (dashed) models.

Figure 5

As in Fig. 1, in the string frame.

Figure 6

As in Fig. 2, in the string frame.

Figure 7

As in Fig. 3, in the string frame.

Figure 8

As in Fig. 4, in the string frame.