Von Neumann stability of modified loop quantum cosmologies

Understand

Von Neumann stability analysis of quantum difference equations in loop quantized spacetimes has often proved useful to understand viability of quantizations and whether general relativistic description is recovered at small spacetime curvatures.

• We use this technique to analyze the infra-red behavior of quantum Hamiltonian constraint in recently explored modifications of loop quantum cosmology: mLQC-I and mLQC-II, for the spatially flat FLRW model.
• We investigate the behavior for $\mu_o$ scheme, where minimum area of loops in quantization procedure does not take physical metric in to account, and the $\bar \mu$ scheme where quantization procedure uses physical metric.
• The fate of stability of quantum difference equations is tested for massless scalar field as well as with inclusion of a positive cosmological constant.