Avoidance of future singularities in loop quantum cosmology

We consider the fate of future singularities in the effective dynamics of loop quantum cosmology. Nonperturbative quantum geometric effects which lead to ${\rho }^2$ modification of the Friedmann equation at high energies result in generic resolution of singularities whenever energy density $\rho$ diverges at future singularities of Friedmann dynamics. Such quantum effects lead to the avoidance of a big rip, which is followed by a recollapsing universe stable against perturbations. Resolution of sudden singularity, the case when pressure diverges but energy density approaches a finite value depends on the ratio of the latter to a critical energy density of the order of the Planck value. If the value of this ratio is greater than unity, the universe escapes the sudden future singularity and becomes oscillatory.

Figure 1

Evolution of the Hubble parameter and the variable $y=\rho /{\rho }_c$ for $w=-1.5$ with initial conditions $y_i=0.01$ and ${\tilde{H}}_i=[y_i(1-y_i){]}^{1/2}$. The big rip singularity is avoided in the presence of loop quantum modifications to the Friedmann dynamics.

Figure 2

Evolution of the Hubble parameter and the variable $y=\rho /{\rho }_c$ for the model (14) with $\tilde{B}=1$, $r={\rho }_0/{\rho }_c=2$ and $\gamma =2$. We choose initial conditions $y_i=0.01$ and ${\tilde{H}}_i=[y_i(1-y_i){]}^{1/2}$. The Hubble parameter $\tilde{H}$ oscillates between $-1/2$ and $1/2$ without reaching the singularity at $\rho ={\rho }_0$.