Loop quantum gravity and the cyclic universe

Loop quantum gravity introduces strong nonperturbative modifications to the dynamical equations in the semiclassical regime, which are responsible for various novel effects, including resolution of the classical singularity in a Friedman universe. Here we investigate the modifications for the case of a cyclic universe potential, assuming that we can apply the four-dimensional loop quantum formalism within the effective four-dimensional theory of the cyclic scenario. We find that loop quantum effects can dramatically alter the near-collision dynamics of the cyclic scenario. In the kinetic-dominated collapse era, the scalar field is effectively frozen by loop quantum friction, so that the branes approach collision and bounce back without actual collision.

Figure 1

Typical cyclic potential [corresponding to parameters $V_0={10}^{-3}$, $m_1=0.2$, and $m_2=20/21$ in Eq. (14)].

Figure 2

The evolution of the scale factor $a(t)$ from a small initial value, for the cyclic potential. The dashed curve shows the standard case, while the solid curve incorporates loop quantum corrections, which stop the branes from colliding. The loop parameters are $j=120$ and $l=3/4$ and the cyclic parameters are $V_0={10}^{-3}$, $m_1=0.2$, and $m_2=20/21$.

Figure 3

Evolution of the moduli field $\phi (t)$ for the case described in Fig. 2.

Figure 4

Evolution of the Hubble rate $H(t)$ for the case described in Fig. 2.