Effective Scenario of Loop Quantum Cosmology

Semiclassical states in isotropic loop quantum cosmology are employed to show that the improved dynamics has the correct classical limit. The effective Hamiltonian for the quantum cosmological model with a massless scalar field is thus obtained, which incorporates also the next to leading order quantum corrections. The possibility that the higher order correction terms may lead to significant departure from the leading order effective scenario is revealed. If the semiclassicality of the model is maintained in the large scale limit, there are great possibilities for a $k=0$ Friedmann expanding universe to undergo a collapse in the future due to the quantum gravity effect. Thus the quantum bounce and collapse may contribute a cyclic universe in the new scenario.

Figure 1

The effective dynamics represented by the observable $v{|}_{\varphi }$ are compared to classical trajectories. In this simulation, the parameters were $G=\hslash =1$, $p_{\varphi }=10000$ with initial data $v_o=100000$, ${ϵ}_o=0.001$.

Figure 2

The cyclic model is compared with expanding and contracting classical trajectories. In this simulation, the parameters were $G=\hslash =1$, $p_{\varphi }=10000$, $ϵ=0.001$ with initial data $v_o=100000$.