Loop Quantum Cosmology

Abstract

This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of effective equations that incorporate the main quantum corrections to the dynamics. We also summarize the theory of quantized metric perturbations propagating in those quantum backgrounds. Finally, we describe how this framework can be applied to obtain a self-consistent extension of the inflationary scenario to incorporate quantum aspects of gravity, and to explore possible phenomenological consequences. * Chapter contribution to "Handbook of Space-time", edited by A. Ashtekar and V. Petkov, Springer-Verlag. † Electronic address: I. AgulloRodenas@damtp.cam.ac.uk

Observational issues in loop quantum cosmology

“…Without going into the actual calculations we give here a few more details, following [17]. The classical theory is described by four variables.…”

“…We focus here, still following [17], on the k = 0 case. Simulations [21,22,23] have shown that effective equations approximate very well the full quantum dynamics (in the sense of expectation values of Dirac observables).…”

Detailed investigation of the duration of inflation in loop quantum cosmology for a Bianchi I universe with different inflaton potentials and initial conditions

“…Loop quantum cosmology (LQC) is a quantum theory inspired by LQG that takes into account the cosmological symmetries. Some recent reviews can be found, e.g., in [11][12][13][14][15][16][17][18][19][20][21][22]. The status of perturbations in LQC is still not fully clear.…”

Phenomenology analysis of duration inflation for tachyon field in loop quantum cosmology

“…There are lots of candidates, one of which is LQC (more recently review, please see [6][7][8]). LQC is a canonical quantization of homogeneous spacetimes based upon the * Electronic address: 87xiaokui@mail.bnu.edu.cn † Electronic address: hexiaokai77@163.com ‡ Electronic address: huangfei@email.arizona.edu § Corresponding author; Electronic address: zhujy@bnu.edu.cn techniques used in loop quantum gravity (LQG) [9,10].…”