Reconstructing the Universe Evolution from Loop Quantum Cosmology Scalar Fields

TL;DR

This paper extends scalar-tensor reconstruction techniques to loop quantum cosmology, analyzing quantum effects on universe evolution, stability, and singularities, with illustrative examples and discussion of classical limits and quantum phenomena.

Contribution

It introduces a generalized scalar-tensor reconstruction method within loop quantum cosmology, highlighting quantum effects, solution classes, and stability conditions.

Findings

Energy density solutions include classical and quantum-specific classes

The quantum framework can lead to finite-time singularities like Big Rip

Classical stability conditions are generalized for quantum cosmology

Abstract

We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we discuss which new features and limitations does the quantum framework brings along, and we use various illustrative examples in order to demonstrate how the method works. As we show the energy density has two different classes of solutions, and one of these yields the correct classical limit while the second captures the quantum phenomena. We study in detail the scalar tensor reconstruction method for both these solutions. Also we discuss some scenarios for which the Hubble rate becomes unbounded at finite time, which corresponds for example in a case that a Big Rip occurs. As we show this issue is non-trivial and we discuss how this case should be treated in a consistent way. Finally, we investigate how the classical stability conditions for the scalar-tensor solutions are generalized in the loop quantum framework.