Effective Scenario of Loop Quantum Cosmology

TL;DR

This paper derives an effective Hamiltonian in loop quantum cosmology that includes quantum corrections, revealing potential for cyclic universe scenarios due to quantum gravity effects.

Contribution

It introduces a new effective Hamiltonian with higher order quantum corrections in isotropic loop quantum cosmology, exploring implications for universe cyclicity.

Findings

Effective Hamiltonian incorporates next-to-leading order quantum corrections.

Higher order corrections may cause significant deviations from leading order predictions.

Quantum effects could induce a cyclic universe with bounce and collapse phases.

Abstract

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 $k=0$ 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.