On Energy Conditions and Stability in Effective Loop Quantum Cosmology
In isotropic loop quantum cosmology, non-perturbatively modified dynamics of a minimally coupled scalar field violates weak, strong and dominant energy conditions when they are stated in terms of equation of state parameter. The violation of strong energy condition helps to have non-singular evolution by evading singularity theorems thus leading to a generic inflationary phase. However, the violation of weak and dominant energy conditions raises concern, as in general relativity these conditions ensure causality of the system and stability of vacuum via Hawking-Ellis conservation theorem. It is shown here that the non-perturbatively modified kinetic term contributes negative pressure but positive energy density. This crucial feature leads to violation of energy conditions but ensures positivity of energy density, as scalar matter Hamiltonian remains bounded from below. It is also shown that the modified dynamics restricts group velocity for inhomogeneous modes to remain sub-luminal thus ensuring causal propagation across spatial distances.