Time asymmetry of cosmic background evolution in loop quantum cosmology

Abstract

We discuss the asymmetry of cosmic background evolution in time with respect to the quantum bounce in the Loop Quantum Cosmology (LQC), employing the value of scalar field at the bounce $\phi_{\rm B}$. We use the Chaotic and the $R^2$ potentials to demonstrate that a possible deflation before the bounce may counteract the inflation that is needed for resolving the cosmological conundrums, so a certain level of time asymmetry is required for the models in LQC. This $\phi_{\rm B}$ is model dependent and closely related to the amounts of deflation and inflation, so we may use observations to confine $\phi_{\rm B}$ and thus the model parameters. With further studies this formalism should be useful in providing an observational testbed for the LQC models.